Chapter 2, Problem 122AP

Interpretation Introduction

(a)

Interpretation:

The given number should be converted into standard scientific notation.

$1/{10}^2$

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 122AP

$1\times {10}^{-2}$.

Explanation of Solution

The given number is $1/{10}^2$ which is equal to 0.01, to write it in scientific notation, decimal is placed after first non-zero digit. After placing the decimal, the decimal is moved two places to the right, thus, power of 10 will be -2. The standard scientific notation will be $1\times {10}^{-2}$.

Interpretation Introduction

(b)

Interpretation:

The given number should be converted into standard scientific notation.

$1/{10}^{-2}$

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 122AP

$1/{10}^{-2}$.

Explanation of Solution

The given number is $1/{10}^{-2}$ which is equal to 100, to write it in scientific notation, decimal is placed after first non-zero digit. After placing the decimal, there will be two digits after the decimal, thus power of 10 will be + 2. The standard scientific notation will be $1\times {10}^2$.

Interpretation Introduction

(c)

Interpretation:

The given number should be converted into standard scientific notation.

$55/{10}^3$

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 122AP

$5.5\times {10}^{-2}$.

Explanation of Solution

The given number is $55/{10}^3$ which is equal to 0.055, to write it in scientific notation, decimal is placed after first non-zero digit. After placing the decimal, the decimal is moved two places to the right, thus, power of 10 will be -2. The standard scientific notation will be $5.5\times {10}^{-2}$.

Interpretation Introduction

(d)

Interpretation:

The given number should be converted into standard scientific notation.

$(3.1\times {10}^6)/{10}^{-3}$

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 122AP

$3.1\times {10}^3$.

Explanation of Solution

The given number is $(3.1\times {10}^6)/{10}^{-3}$, to write it in scientific notation, decimal is placed after first non-zero digit. In given number, decimal is already placed after first non-zero digit, thus the overall power of 10 will be + 3. Hence, the standard scientific notation will be $3.1\times {10}^3$.

Interpretation Introduction

(e)

Interpretation:

The given number should be converted into standard scientific notation.

${({10}^6)}^{1/2}$

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 122AP

$1\times {10}^3$.

Explanation of Solution

The given number is ${({10}^6)}^{1/2}$ which is equal to 1000, to write it in scientific notation, decimal is placed after first non-zero digit. After placing the decimal, there will be three digits after the decimal, thus power of 10 will be + 3. The standard scientific notation will be $1\times {10}^3$.

Interpretation Introduction

(f)

Interpretation:

The given number should be converted into standard scientific notation.

$({10}^6)({10}^4)/({10}^2)$

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 122AP

$1\times {10}^8$.

Explanation of Solution

The given number is $({10}^6)({10}^4)/({10}^2)$ which is equal to 100000000, to write it in scientific notation, decimal is placed after first non-zero digit. After placing the decimal, there will be eight digits after the decimal, thus power of 10 will be + 8. The standard scientific notation will be $1\times {10}^8$.

Interpretation Introduction

(g)

Interpretation:

The given number should be converted into standard scientific notation.

$1/0.0034$

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 122AP

$2.9\times {10}^2$.

Explanation of Solution

The given number is $1/0.0034$ which is equal to $0.29411\times {10}^3$, to write it in scientific notation, decimal is placed after first non-zero digit. Thus, the decimal moved to one place to the right and power of 10 will be decreased by 1 unit, thus overall power of 10 will be + 3-1 = 2. The standard scientific notation will be $2.9\times {10}^2$.

Interpretation Introduction

(h)

Interpretation:

The given number should be converted into standard scientific notation.

$3.453/{10}^{-4}$

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 122AP

$3.453\times {10}^4$.

Explanation of Solution

The given number is $3.453/{10}^{-4}$ which is equal to 0.0003453, to write it in scientific notation, decimal is placed after first non-zero digit. Thus, the decimal moved to four places to the right and power of 10 will be decreased by 4 units, thus, the standard scientific notation will be $3.453\times {10}^4$.