Chapter 2, Problem 116AP

Interpretation Introduction

(a)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$102$.

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 to Problem 116AP

The decimal will placed after first digit and the exponent of the power of 10 is positive that is + 2 imply two digits are present after decimal.

Explanation of Solution

The given number is $102$. First convert it into scientific notation. Decimal is placed after first digit, after placing the decimal, there will be two digits after the decimal thus, power of 10 will be + 2 and scientific notation will be $1.02\times {10}^2$. Thus, the exponent of the power of 10 is positive that is + 2.

Interpretation Introduction

(b)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$0.00000000003489$.

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 to Problem 116AP

The decimal will move eleven places to the right and the exponent of the power of 10 is negative that is -11.

Explanation of Solution

The given number is $0.00000000003489$. First convert it into scientific notation. Decimal is placed after first non-zero digit, thus, decimal will move eleven places to the right. Since, the decimal is moving to right, power of 10 will be decreased by 11 units and scientific notation will be $3.489\times {10}^{-11}$. Thus, exponent of the power of 10 is negative that is -11.

Interpretation Introduction

(c)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$2500$.

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 to Problem 116AP

The decimal will placed after first digit and the exponent of the power of 10 is positive that is + 3 imply three digits are present after decimal.

Explanation of Solution

The given number is $2500$. First convert it into scientific notation. Decimal is placed after first digit, after placing the decimal, there will be three digits after the decimal thus, power of 10 will be + 3 and scientific notation will be $2.5\times {10}^3$. Thus, the exponent of the power of 10 is positive that is + 3.

Interpretation Introduction

(d)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$0.00003489$.

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 to Problem 116AP

The decimal will move five places to the right and the exponent of the power of 10 is negative that is -5.

Explanation of Solution

The given number is $0.00003489$. First convert it into scientific notation. Decimal is placed after first non-zero digit, thus, decimal will move five places to the right. Since, the decimal is moving to right, power of 10 will be decreased by five units and scientific notation will be $3.489\times {10}^{-5}$. Thus, exponent of the power of 10 is negative that is -5.

Interpretation Introduction

(e)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$398,000$.

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 to Problem 116AP

The decimal will placed after first digit and the exponent of the power of 10 is positive that is + 5 imply five digits are present after decimal.

Explanation of Solution

The given number is $398,000$. First convert it into scientific notation. Decimal is placed after first digit, after placing the decimal, there will be five digits after the decimal thus, power of 10 will be + 5 and scientific notation will be $3.98\times {10}^5$. Thus, the exponent of the power of 10 is positive that is + 5.

Interpretation Introduction

(f)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$1$.

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 to Problem 116AP

The exponent of the power of 10 is zero.

Explanation of Solution

The given number is $1$. First convert it into scientific notation that is $1\times {10}^0$. Thus, the exponent of the power of 10 is zero.

Interpretation Introduction

(g)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$0.3489$.

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 to Problem 116AP

The decimal will move one place to the right and the exponent of the power of 10 is negative that is -1.

Explanation of Solution

The given number is $0.3489$. First convert it into scientific notation. Decimal is placed after first non-zero digit, thus, decimal will move one place to the right. Since, the decimal is moving to right, power of 10 will be decreased by 1 unit and scientific notation will be $3.489\times {10}^{-1}$. Thus, exponent of the power of 10 is negative that is -5.

Interpretation Introduction

(h)

Interpretation:

The number of places does decimal have to be moved to express the number in standard scientific notation should be determined along with identify whether the exponent of the power of 10 is positive or negative.

$0.0000003489$.

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 to Problem 116AP

The decimal will move seven places to the right and the exponent of the power of 10 is negative that is -7.

Explanation of Solution

The given number is $0.0000003489$. First convert it into scientific notation. Decimal is placed after first non-zero digit, thus, decimal will move seven places to the right. Since, the decimal is moving to right, power of 10 will be decreased by 7 units and scientific notation will be $3.489\times {10}^{-7}$. Thus, exponent of the power of 10 is negative that is -7.