Chapter PSS, Problem 27E

Interpretation Introduction

(a)

Interpretation:

The given measurement is to be divided and the answer is rounded off to the proper significant digit.

Concept introduction:

In the multiplication or division of measurements, the answer is found to be limited by the measurement value with the lowest number of significant digits. The final unit in division is the ratio of the units of each data.

Answer to Problem 27E

The answer up to two significant digits is $8.\text{8 }\text{g}/\text{mL}$.

Explanation of Solution

The given measurement is $66.\text{3 g}/7.\text{5 mL}$. The measurement of $66.\text{3 g}$ has three significant digits and $\text{7}\text{.5 mL}$ has two significant digits. Therefore, the product or the final answer must be limited to two significant digits.

The division of the given measurement is shown below.

$66.\text{3 g}/7.\text{5 mL}=8.\text{84 }\text{g}/\text{mL}$

Hence, the rounded off answer up to two significant digits is $8.\text{8 }\text{g}/\text{mL}$.

Conclusion

The answer up to two significant digits is $8.\text{8 }\text{g}/\text{mL}$.

Interpretation Introduction

(b)

Interpretation:

The given measurement is to be divided and the answer is rounded off to the proper significant digit.

Concept introduction:

In the multiplication or division of measurements, the answer is found to be limited by the measurement value with the lowest number of significant digits. The final unit in division is the ratio of the units of each data.

Answer to Problem 27E

The answer up to two significant digits is $\text{3}\text{.0 }\text{g}/\text{mL}$.

Explanation of Solution

The given measurement is $\text{12}\text{.5 g}/\text{4}\text{.1 mL}$. The measurement of $\text{12}\text{.5 g}$ has three significant digits and $\text{4}\text{.1 mL}$ has two significant digits. Therefore, the product or the final answer must be limited to two significant digits.

The division of the given measurement is shown below.

$\text{12}\text{.5 g}/\text{4}\text{.1 mL}=3.048\text{g}/\text{mL}$

Hence, the rounded off answer up to two significant digits is $\text{3}\text{.0 }\text{g}/\text{mL}$.

Conclusion

The answer up to two significant digits is $\text{3}\text{.0 }\text{g}/\text{mL}$.

Interpretation Introduction

(c)

Interpretation:

The given measurement is to be divided and the answer is rounded off to the proper significant digit.

Concept introduction:

In the multiplication or division of measurements, the answer is found to be limited by the measurement value with the lowest number of significant digits. The final unit in division is the ratio of the units of each data.

Answer to Problem 27E

The answer up to three significant digits is $\text{4}\text{.26 }\text{g}/\text{mL}$.

Explanation of Solution

The given measurement is $\text{42}\text{.620 g}/\text{10}\text{.0 mL}$. The measurement of $\text{42}\text{.620 g}$ has five significant digits and $\text{10}\text{.0 mL}$ has three significant digits. Therefore, the product or the final answer must be limited to three significant digits.

The division of the given measurement is shown below.

$\text{42}\text{.620 g}/\text{10}\text{.0 mL}=4.262\text{g}/\text{mL}$

Hence, the rounded off answer up to three significant digits is $\text{4}\text{.26 }\text{g}/\text{mL}$.

Conclusion

The answer up to three significant digits is $\text{4}\text{.26 }\text{g}/\text{mL}$.

Interpretation Introduction

(d)

Interpretation:

The given measurement is to be divided and the answer is rounded off to the proper significant digit.

Concept introduction:

In the multiplication or division of measurements, the answer is found to be limited by the measurement value with the lowest number of significant digits. The final unit in division is the ratio of the units of each data.

Answer to Problem 27E

The answer up to four significant digits is $\text{9}\text{.124 }\text{g}/\text{mL}$.

Explanation of Solution

The given measurement is $\text{91}\text{.235 g}/\text{10}\text{.00 mL}$. The measurement of $\text{91}\text{.235 g}$ has five significant digits and $\text{10}\text{.00 mL}$ has four significant digits. Therefore, the product or the final answer must be limited to four significant digits.

The division of the given measurement is shown below.

$\text{91}\text{.235 g}/\text{10}\text{.00 mL}=9.1235\text{g}/\text{mL}$

Hence, the rounded off answer up to four significant digits is $\text{9}\text{.124 }\text{g}/\text{mL}$.

Conclusion

The answer up to four significant digits is $\text{9}\text{.124 }\text{g}/\text{mL}$.