Chapter 2, Problem 2.52EP

Carry out the following additions and subtractions, expressing your answer to the correct number of significant figures. Assume that all numbers are measured numbers.

1. a. 237 + 37.0 + 7.0
2. b. 4.000 + 4.002 + 4.20
3. c. 235.45 + 37 + 36.4
4. d. 3.111 – 2.07

Interpretation Introduction

Interpretation:

The answer for the given addition problem $\text{237}\text{+}\text{37}\text{.0}\text{+}\text{7}\text{.0}$ 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 addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.52EP

When the problem $\text{237}\text{+}\text{37}\text{.0}\text{+}\text{7}\text{.0}$ is solved, the answer (281) is obtained.  But there are no inferred decimal points to say the significant figures.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, $\text{237}\text{+}\text{37}\text{.0}\text{+}\text{7}\text{.0}$, the obtained answer is 281,  But in this problem there are no decimal points to determine the significant figure.

$\begin{array}{l}237\to significantfigure=nodecimal\text{point}\text{to}\text{determine}\\ 37.0\to significantfigure=1\\ +7.0\to significantfigure=1\\ \overline{281}\to significantfigure=\text{no digit to the right of the inferred decimal point}\end{array}$

Conclusion

The answer obtained is 281, but there are no decimal points in the measurements in the problem to identify the significant figures.

Interpretation Introduction

Interpretation:

The answer for the given addition problem $\text{4}\text{.000}\text{+}\text{4}\text{.002}\text{+}\text{4}\text{.20}$ 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 addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.52EP

When the problem $\text{4}\text{.000}\text{+}\text{4}\text{.002}\text{+}\text{4}\text{.20}$ is solved, the answer (12.20) is obtained with two significant figures to the right side of the decimal point.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, $\text{4}\text{.000}\text{+}\text{4}\text{.002}\text{+}\text{4}\text{.20}$, $\text{4}\text{.000}$ has three significant figures to the right side of the decimal point, whereas $\text{4}\text{.002}$ and $\text{4}\text{.20}$ has three significant figures and two significant figures to the right side of the decimal point respectively.  Hence the fewest significant figure here is two.

$\begin{array}{l}4.000\to significantfigure=3\\ 4.002\to significantfigure=3\\ +4.20\to significantfigure=2\\ \overline{12.20}\to significantfigure=\text{two digits to the right of the inferred decimal point}\end{array}$

Conclusion

The fewest significant figure in the measurements of the problem is two. The answer obtained is 12.20 with two significant figures.

Interpretation Introduction

Interpretation:

The answer for the given addition problem $\text{235}\text{.45}\text{+}\text{37}\text{+}\text{36}\text{.4}$ 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 addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.52EP

When the problem $\text{235}\text{.45}\text{+}\text{37}\text{+}\text{36}\text{.4}$ is solved, the answer (309) is obtained.  But there are no inferred decimal points to say the significant figures.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, $\text{235}\text{.45}\text{+}\text{37}\text{+}\text{36}\text{.4}$, the obtained answer is 309.  But in this problem there are no decimal points to determine the significant figures.

$\begin{array}{l}235.45\to significantfigure=2\\ 37\to significantfigure=nodecimal\text{point}\text{to}\text{determine}\\ +36.4\to significantfigure=1\\ \overline{309}\to significantfigure=\text{no digit to the right of the inferred decimal point}\end{array}$

Conclusion

The answer obtained is 309, but there are no decimal points in the measurements in the problem to identify the significant figures.

Interpretation Introduction

Interpretation:

The answer for the given subtraction problem $\text{3}\text{.111}\text{+}\text{2}\text{.07}$ 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 addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.

Answer to Problem 2.52EP

When the problem $\text{3}\text{.111}\text{+}\text{2}\text{.07}$ is solved, the answer (1.04) is obtained with two significant figures to the right side of the decimal point.

Explanation of Solution

The number of significant figures in the answer after solving addition or subtraction problem is same as the number of fewest significant figures present to the right side of the decimal point of the measurement.  For the problem, $\text{3}\text{.111}\text{+}\text{2}\text{.07}$, $\text{3}\text{.111}$ has three significant figures to the right side of the decimal point, whereas $\text{2}\text{.07}$ has two significant figures to the right side of the decimal point.  Hence the fewest significant figure here is two.

$\begin{array}{l}3.111\to significantfigure=3\\ +2.07\to significantfigure=2\\ \overline{1.04}\to significantfigure=\text{two digits to the right of the inferred decimal point}\end{array}$

Conclusion

The fewest significant figure in the measurements of the problem is two.  The answer obtained is 1.04 with two significant figures.