Chapter 2, Problem 2.49EP

(a)

Interpretation Introduction

Interpretation:

The answer of multiplication problem $\text{2}\text{.0000}\text{×}\text{2}\text{.00}\text{×}\text{0}\text{.0020}$ must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.

Answer to Problem 2.49EP

When the problem $\text{2}\text{.0000}\text{×}\text{2}\text{.00}\text{×}\text{0}\text{.0020}$ is solved, the answer (0.0080) obtained will have two significant figures.

Explanation of Solution

The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.  In the problem, $\text{2}\text{.0000}\text{×}\text{2}\text{.00}\text{×}\text{0}\text{.0020}$, $\text{2}\text{.0000}$ has significant figure of five, while $\text{2}\text{.00}$ has three significant figures and $\text{0}\text{.0020}$ has two significant figures.  Hence the lowest significant figure from the above measurement is two, so the answer obtained will have two significant figures.

  $\begin{array}{l}significantfigure=5significantfigure=3significantfigure=2\\ \uparrow \uparrow \uparrow \\ \text{2}\text{.0000}\text{×}\text{2}\text{.00}\text{×}\text{0}\text{.0020}\text{=}\text{0}\text{.0080}\\ \downarrow \\ significantfigure=2\end{array}$

Conclusion

The answer will have two significant figures, if the problem $\text{2}\text{.0000}\text{×}\text{2}\text{.00}\text{×}\text{0}\text{.0020}$ is solved.

(b)

Interpretation Introduction

Interpretation:

The answer of multiplication problem $\text{4}\text{.1567}\text{×}\text{0}\text{.00345}$ must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.

Answer to Problem 2.49EP

When the problem $\text{4}\text{.1567}\text{×}\text{0}\text{.00345}$ is solved, the answer (0.0143) obtained will have two significant figures.

Explanation of Solution

The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.  In the problem, $\text{4}\text{.1567}\text{×}\text{0}\text{.00345}$, $\text{4}\text{.1567}$ has significant figure of five, while $\text{0}\text{.00345}$ has three significant.  Hence the lowest significant figure from the above measurement is three, so the answer obtained will have three significant figures.

  $\begin{array}{l}significantfigure=5significantfigure=3\\ \uparrow \uparrow \\ \text{4}\text{.1567}\text{×}\text{0}\text{.00345}\text{=}\text{0}\text{.0143}\\ \downarrow \\ significantfigure=3\end{array}$

Conclusion

The answer will have two significant figures, if the problem $\text{4}\text{.1567}\text{×}\text{0}\text{.00345}$ is solved.

(c)

Interpretation Introduction

Interpretation:

The answer of multiplication problem $0.0037\times 3700\times 1.001$ must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.

Answer to Problem 2.49EP

When the problem $0.0037\times 3700\times 1.001$ is solved, the answer (14) obtained will have  two significant figures.

Explanation of Solution

The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.  In the problem $0.0037\times 3700\times 1.001$, $0.0037$ has significant figure of two, while $3700$ has two significant figures and $1.001$ has significant figure of four.  Hence the lowest significant figure from the above measurement is two, so the answer obtained will have two significant figures.

  $\begin{array}{l}significantfigure=2significantfigure=2significantfigure=2\\ \uparrow \uparrow \uparrow \\ \text{0}\text{.0037}\text{×}\text{3700}\text{×}\text{1}\text{.001}\text{=}\text{14}\\ \downarrow \\ significantfigure=4\end{array}$

Conclusion

The answer will have two significant figures, if the problem $0.0037\times 3700\times 1.001$ is solved.

(d)

Interpretation Introduction

Interpretation:

The answer of division problem $6.00÷33.0$ must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.

Answer to Problem 2.49EP

When the problem $6.00÷33.0$ is solved, the answer (0.182) obtained will have  three significant figures.

Explanation of Solution

The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.  In the problem $6.00÷33.0$, $6.00$ has significant figure of three, while $33.0$ has three significant figures.  Hence the lowest significant figure from the above measurement is three, so the answer obtained will have three significant figures.

  $\begin{array}{l}significantfigure=3significantfigure=3\\ \uparrow \uparrow \\ \text{6}\text{.00}÷\text{33}\text{.0}\text{=}\text{0}\text{.182}\\ \downarrow \\ significantfigure=3\end{array}$

Conclusion

The answer will have three significant figures if the problem $6.00÷33.0$ is solved.

(e)

Interpretation Introduction

Interpretation:

The answer of division problem $\text{530,000}\text{÷}\text{465,300}$ must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.

Answer to Problem 2.49EP

When the problem $\text{530,000}\text{÷}\text{465,300}$ is solved, the answer (1.1) obtained will have two significant figures.

Explanation of Solution

The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.  In the problem $\text{530,000}\text{÷}\text{465}\text{.300}$, $\text{530,000}$ has significant figure of two, while $\text{465,300}$ has four significant figures.  Hence the lowest significant figure from the above measurement is two, so the answer obtained will have two significant figures.

  $\begin{array}{l}significantfigure=2significantfigure=2\\ \uparrow \uparrow \\ \text{530000}÷\text{465300}\text{=}\text{1}\text{.1}\\ \downarrow \\ significantfigure=4\end{array}$

Conclusion

The answer will have two significant figures if the problem $\text{530,000}\text{÷}\text{465,300}$ is solved.

(f)

Interpretation Introduction

Interpretation:

The answer of multiplication and division problem $\left(\text{4670}\text{× 3}\text{.00}\right)\text{÷}\text{2}\text{.450}$ must be expressed to the correct number of significant figures.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.

Answer to Problem 2.49EP

When the problem $\left(\text{4670}\text{× 3}\text{.00}\right)\text{÷}\text{2}\text{.450}$ is solved, the answer (5720) obtained will have three significant figures.

Explanation of Solution

The number of significant figures in the answer after solving a multiplication or division problem is same as the number of fewest significant figures present in the measurement.  In the problem $\left(\text{4670}\text{× 3}\text{.00}\right)\text{÷}\text{2}\text{.450}$, $\text{4670}$ has significant figure of three, while $\text{3}\text{.00}$ has three significant figures and $\text{2}\text{.450}$ has significant figure of four.  Hence the lowest significant figure from the above measurement is three, so the answer obtained will have three significant figures.

  $\begin{array}{l}significantfigure=3significantfigure=3significantfigure=3\\ \uparrow \uparrow \uparrow \\ \left(4670\times 3.00\right)÷\text{2}\text{.450}\text{=}\text{5720}\\ \downarrow \\ significantfigure=4\end{array}$

Conclusion

The answer will have three significant figures if the problem $\left(\text{4670}\text{× 3}\text{.00}\right)\text{÷}\text{2}\text{.450}$ is solved.