To convert the given number 0.0008917 to standard scientific notation. Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10. For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Question

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Answer 1

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

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Answer 2

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

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Answer 3

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

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Answer 4

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

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Answer 5

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Answer 6

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

Answer 7

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 8

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

Answer 13

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 14

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 15

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 20

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 21

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 22

(c)

Expert Solution

Answer to Problem 14CR

4913

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 27

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

Answer 28

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 29

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

Answer 34

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

Answer 35

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 36

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

Answer 41

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Answer 42

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 43

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Answer 44

(f)

Expert Solution

Answer 45

(f)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8