The mass of two samples of copper were measured. What is the total mass, reported to the appropriate number of significant figures?
[tex]
\begin{array}{r}
1.6524 g \\
+\quad 5.67 g \\
\hline[?] g
\end{array}
[/tex]
Answer (2)
Add the two masses: 1.6524 + 5.67 = 7.3224 .
Identify the least precise decimal place: hundredths place.
Round the result to the hundredths place: 7.3224 ≈ 7.32 .
The total mass, reported to the appropriate number of significant figures, is 7.32 g.
Explanation
Problem Analysis We are asked to add two masses and report the result to the appropriate number of significant figures. The given masses are 1.6524 g and 5.67 g.
Adding the Masses First, we add the two masses: 1.6524 + 5.67 = 7.3224
Significant Figures Next, we determine the number of significant figures in each number. 1.6524 has 5 significant figures, and 5.67 has 3 significant figures. When adding numbers, the result should be rounded to the least precise decimal place. 1.6524 is precise to the ten-thousandths place, while 5.67 is precise to the hundredths place. Therefore, we must round the result to the hundredths place.
Rounding the Result Rounding 7.3224 to the hundredths place, we get 7.32.
Final Answer Therefore, the total mass, reported to the appropriate number of significant figures, is 7.32 g.
Examples
In a lab setting, you might need to combine precise amounts of chemicals. If you have 1.6524 grams of one chemical and add 5.67 grams of another, you need to know the total mass to the correct precision. Reporting the total mass as 7.32 grams ensures your measurements are accurate and reliable, which is crucial for the success of the experiment. This principle of significant figures helps maintain the integrity of scientific data.
The total mass of the two copper samples is calculated as 7.3224 g, which is then rounded to 7.32 g because the least precise measurement is in the hundredths place. Thus, the final mass is reported as 7.32 g to reflect the appropriate number of significant figures. This approach ensures accuracy in scientific measurements.
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