Chapter 2, Problem 121AP

Interpretation Introduction

(a)

Interpretation:

The given number should be converted into standard scientific notation.

$102.3\times {10}^{-5}$

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 121AP

$1.023\times {10}^{-2}$.

Explanation of Solution

The given number is $102.3\times {10}^{-5}$, 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 increased by + 3 and scientific notation will be $1.023\times {10}^{-2}$ (-5+3 = -2).

Interpretation Introduction

(b)

Interpretation:

The given number should be converted into standard scientific notation.

$32.03\times {10}^{-3}$

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 121AP

$3.203$.

Explanation of Solution

The given number is $32.03\times {10}^{-3}$, to write it in scientific notation, decimal is placed after first non-zero digit. After placing the decimal, thus, three units are added to the power of 10. The power of 10 becomes + 3 and scientific notation will be $3.203$ as power of 10 is -3 and after placing the decimal then + 3 is added to the power of 10, thus power of 10 is equal to 0. Hence, $3.203$ is the standard scientific notation.

Interpretation Introduction

(c)

Interpretation:

The given number should be converted into standard scientific notation.

$59933\times {10}^2$

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 121AP

$5.9933\times {10}^6$.

Explanation of Solution

The given number is $59933\times {10}^2$, to write it in scientific notation, decimal is placed after first non-zero digit. Thus, after placing the decimal, there will be four digits after the decimal, thus, power of 10 will be increased by four units, and overall power of 10 will be + 2+4 = 6. Thus, standard scientific notation is $5.9933\times {10}^6$.

Interpretation Introduction

(d)

Interpretation:

The given number should be converted into standard scientific notation.

$599.33\times {10}^4$

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 121AP

$5.9933\times {10}^8$.

Explanation of Solution

The given number is $599.33\times {10}^4$, to write it in scientific notation, decimal is placed after first non-zero digit. Thus, after placing the decimal, there will be four digits after the decimal, thus, power of 10 will be increased by four units, and overall power of 10 will be + 4+4 = 8. Thus, standard scientific notation is $5.9933\times {10}^8$.

Interpretation Introduction

(e)

Interpretation:

The given number should be converted into standard scientific notation.

$5993.3\times {10}^3$

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 121AP

$5.9933\times {10}^7$.

Explanation of Solution

The given number is $5993.3\times {10}^3$, to write it in scientific notation, decimal is placed after first non-zero digit. Thus, after placing the decimal, there will be four digits after the decimal, thus, power of 10 will be increased by four units, and overall power of 10 will be + 3+4 = 7. Thus, standard scientific notation is $5.9933\times {10}^7$.

Interpretation Introduction

(f)

Interpretation:

The given number should be converted into standard scientific notation.

$2054\times {10}^{-1}$

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 121AP

$2.054\times {10}^2$.

Explanation of Solution

The given number is $2054\times {10}^{-1}$, 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 and thus, overall power of 10 will be + 3-1=+2. Hence, standard scientific notation is $2.054\times {10}^2$.

Interpretation Introduction

(g)

Interpretation:

The given number should be converted into standard scientific notation.

$32,000,000\times {10}^{-6}$

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 121AP

$3.2\times {10}^1$.

Explanation of Solution

The given number is $32,000,000\times {10}^{-6}$, to write it in scientific notation, decimal is placed after first non-zero digit. After placing the decimal, there will be seven digits after the decimal thus, power of 10 will be + 7 and thus, overall power of 10 will be + 7-6=+1. Hence, standard scientific notation is $3.2\times {10}^1$.

Interpretation Introduction

(h)

Interpretation:

The given number should be converted into standard scientific notation.

$59.933\times {10}^5$

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 121AP

$5.9933\times {10}^9$.

Explanation of Solution

The given number is $59.933\times {10}^5$, to write it in scientific notation, decimal is placed after first non-zero digit. Thus, after placing the decimal, there will be four digits after the decimal, thus, power of 10 will be increased by four units, and overall power of 10 will be + 4+5 = 9. Thus, standard scientific notation is $5.9933\times {10}^9$.