Chapter 3, Problem 16CR

Interpretation Introduction

(a)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The answer will have two significant figures.

Explanation of Solution

The answer will have two significant figures, because number $2.1$ has only two significant figures. In multiplication and division, limiting term is the one with smallest number of significant figures.

Interpretation Introduction

(b)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The answer should have two significant figures.

Explanation of Solution

The answer will have two significant figures. According to Bodmas rule, if an expression contains brackets, we have to first solve or simplify the bracket then division, multiplication, addition and subtraction from left to right. So in the calculation divisor has addition calculation within brackets. However after the simplification divisor should have four significant figures. After the simplification, there is a division calculation. Because number $5.2$ has only two significant figures the final answer should have two significant figures. In multiplication and division, limiting term is the one with smallest number of significant figures.

Interpretation Introduction

(c)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The final answer should have two decimal places and three significant figures.

Explanation of Solution

In addition and subtraction, limiting term is the one with smallest number of decimal places. Because $2.11$ has only two decimal places, final answer should also have two decimal places with three significant figures.

Interpretation Introduction

(d)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The answer should have three significant figures.

Explanation of Solution

The answer will have three significant figures. According to Bodmas rule, if an expression contains brackets, we have to first solve or simplify the bracket then division, multiplication, addition and subtraction from left to right. So in the calculation there is an addition calculation within brackets. After the simplification it should have two decimal places as $2.11$ has two decimal places and three significant figures. After the simplification, there is a multiplication calculation. Because the simplified number has only three significant figures the final answer should have three significant figures. In multiplication and division, limiting term is the one with smallest number of significant figures.

Interpretation Introduction

(e)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The answer should have one significant figure.

Explanation of Solution

The answer will have one significant figure. In addition and subtraction, limiting term is the one with smallest decimal places. Because $9$ have no decimal places, final answer should have no decimal places. So it should have one significant figure.

Interpretation Introduction

(f)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The answer should have two significant figures.

Explanation of Solution

The answer will have two significant figures. According to Bodmas rule, if an expression contains brackets, we have to first solve or simplify the bracket then division, multiplication, addition and subtraction from left to right. So in the calculation there is an addition calculation within brackets. After the simplification it should have one decimal place as $2.7$ has one decimal place and two significant figures. After the simplification, there is a multiplication calculation. Because the simplified number has only two significant figures the final answer should have two significant figures. In multiplication and division, limiting term is the one with smallest number of significant figures.

Interpretation Introduction

(g)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The final answer should have two significant figures.

Explanation of Solution

In multiplication and division, limiting term is the one with smallest number of significant figures. Because $0.15$ has only two significant figures, final answer should also have two significant figures.

Interpretation Introduction

(h)

Interpretation:

In the given calculation, number of significant figures that the final answer should have, following the calculation should be determined, without performing the actual calculation.

Concept Introduction:

In calculations, for multiplication or division, the number of significant figures in the result is same as that in the measurement with the smallest number of significant figures. So the measurement is limiting because it limits the number of significant figures in the results. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Answer to Problem 16CR

The final answer should have one decimal place with three significant figures.

Explanation of Solution

In addition and subtraction, limiting term is the one with smallest number of decimal places. Because $42.1$ has only one decimal place, final answer should also have one decimal places. So final answer will have three significant figures.