Chapter 2, Problem 139AP

Interpretation Introduction

(a)

Interpretation:

The number of significant digits in the answer should be determined by evaluating the given expression.

$(0.0432)(2.909)(4.43\times {10}^8)$.

Concept Introduction:

During addition or subtraction, the final answer should be rounded off for minimum number of digits after the decimal for more accuracy.

Decimal place is the position of digit right to the decimal point.

In division and multiplication, the calculated values are always rounded up to minimum number of significant figures.

Initially the calculation is carry out without considering the significant figures, the rounding off is done after the completion of all the calculations.

Rules for rounding off numbers are as follows:

1. If the number to be rounded off is followed by digit 5 or greater than 5, the number will be rounded up.
2. If the number to be rounded off is followed by digit zero or less than 5, the number will be rounded down.

Answer to Problem 139AP

$0.557\times {10}^8$.

Explanation of Solution

The expression is $(0.0432)(2.909)(4.43\times {10}^8)$. By calculating it we get, $0.556712784\times {10}^8$

In multiplication, the number of significant figures in final answer should be equal to the minimum number of significant figures in the calculation. The number with minimum number of significant figure is $4.43\times {10}^8$ thus, minimum number of significant figure is 3, thus, final answer should be rounded off up to three significant figures which is equal to $0.557\times {10}^8$.

Interpretation Introduction

(b)

Interpretation:

The number of significant digits in the answer should be determined by evaluating the given expression.

$(0.8922)/[(0.00932)(4.03\times {10}^2)]$

Concept Introduction:

During addition or subtraction, the final answer should be rounded off for minimum number of digits after the decimal for more accuracy.

Decimal place is the position of digit right to the decimal point.

In division and multiplication, the calculated values are always rounded up to minimum number of significant figures.

Initially the calculation is carry out without considering the significant figures, the rounding off is done after the completion of all the calculations.

Rules for rounding off numbers are as follows:

1. If the number to be rounded off is followed by digit 5 or greater than 5, the number will be rounded up.
2. If the number to be rounded off is followed by digit zero or less than 5, the number will be rounded down.

Answer to Problem 139AP

$23.74\times {10}^{-2}$.

Explanation of Solution

The given expression is $(0.8922)/[(0.00932)(4.03\times {10}^2)]$. By calculating it we get, $23.7542465\times {10}^{-2}$

In multiplication and division, the number of significant figures in final answer should be equal to the minimum number of significant figures in the calculation. The number with minimum number of significant figure is $0.8922$ thus, minimum number of significant figure is 4, thus, final answer should be rounded off up to four significant figures which is equal to $23.74\times {10}^{-2}$.

Interpretation Introduction

(c)

Interpretation:

The number of significant digits in the answer should be determined by evaluating the given expression.

$(3.923\times {10}^2)(2.94)(4.093\times {10}^{-3})$

Concept Introduction:

During addition or subtraction, the final answer should be rounded off for minimum number of digits after the decimal for more accuracy.

Decimal place is the position of digit right to the decimal point.

In division and multiplication, the calculated values are always rounded up to minimum number of significant figures.

Initially the calculation is carry out without considering the significant figures, the rounding off is done after the completion of all the calculations.

Rules for rounding off numbers are as follows:

1. If the number to be rounded off is followed by digit 5 or greater than 5, the number will be rounded up.
2. If the number to be rounded off is followed by digit zero or less than 5, the number will be rounded down.

Answer to Problem 139AP

$47.2\times {10}^{-1}$.

Explanation of Solution

The given expression is $(3.923\times {10}^2)(2.94)(4.093\times {10}^{-3})$. By calculating it we get, $47.20710666\times {10}^{-1}$

In multiplication, the number of significant figures in final answer should be equal to the minimum number of significant figures in the calculation. The number with minimum number of significant figure is $2.94$ thus, minimum number of significant figure is 3, thus, final answer should be rounded off up to three significant figures which is equal to $47.2\times {10}^{-1}$.

Interpretation Introduction

(d)

Interpretation:

The number of significant digits in the answer should be determined by evaluating the given expression.

$(4.9211)(0.04434)/[(0.000934)(2.892\times {10}^{-7})]$

Concept Introduction:

During addition or subtraction, the final answer should be rounded off for minimum number of digits after the decimal for more accuracy.

Decimal place is the position of digit right to the decimal point.

In division and multiplication, the calculated values are always rounded up to minimum number of significant figures.

Initially the calculation is carry out without considering the significant figures, the rounding off is done after the completion of all the calculations.

Rules for rounding off numbers are as follows:

1. If the number to be rounded off is followed by digit 5 or greater than 5, the number will be rounded up.
2. If the number to be rounded off is followed by digit zero or less than 5, the number will be rounded down.

Answer to Problem 139AP

$80.78\times {10}^7$.

Explanation of Solution

The given expression is $(4.9211)(0.04434)/[(0.000934)(2.892\times {10}^{-7})]$. By calculating it we get, $80.78164899997334\times {10}^7$

In multiplication and division, the number of significant figures in final answer should be equal to the minimum number of significant figures in the calculation. The number with minimum number of significant figure is $2.892\times {10}^{-7}$ thus, minimum number of significant figure is 4, thus, final answer should be rounded off up to four significant figures which is equal to $80.78\times {10}^7$.