Question

A sample was weighed using two different balances. The results were (i) $\text{3}\text{.929 g}$(ii) $\text{4}\text{.0 g}$. How would the weight of the sample be reported?
A. $\text{3}\text{.929 g}$
B.3 g
C.$\text{3}\text{.9 g}$
D.$\text{3}\text{.93 g}$

Answer 1

The expression of a decimal number follows the rules for the significant numbers. The precision in measurement of a number refers to how close an agreement is between repeated measurements. The accuracy is defined as the closeness of the measured value to the correct value.

Complete step by step answer:
From the question it can be seen that among the two given values from the two measurements are ${\text{4}}{\text{.0 g}}$ and ${\text{3}}{\text{.939 g}}$. Among these two values, ${\text{4}}{\text{.0 g}}$ is the more accurate value while ${\text{3}}{\text{.939 g}}$ is the more precise value. We need to report the weight of the sample to be reported from these two. If we round off the second value to two decimal places, then the value becomes ${\text{3}}{\text{.93 g}}$. This is because, as the rule of significant numbers, if the digit to be rounded off is higher than 5, then $\left( { + 1} \right)$ is added to the previous digit while if the digit is smaller than the previous digit.
Here, in the given number, the last digit is 9, which is greater than 5 and hence it can be rounded off easily by adding $\left( { + 1} \right)$ to 2 which makes it ${\text{3}}{\text{.93 g}}$.

Therefore, the sample should be more precisely reported as ${\text{3}}{\text{.93 g}}$ so the correct answer is option D.

Note:
The degree of precision and accuracy of a measuring system are related to the degree of uncertainty of the system. Where, uncertainty is the quantitative measure of how much the measured value deviates from the standard value.