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}{l}
1.6524 g \\
+ 5.67 g \\
\hline
\end{array}
[/tex]
Answer (2)
Add the two masses: 1.6524 + 5.67 = 7.3224 .
Identify the number with the fewest decimal places: 5.67 has two decimal places.
Round the sum to two decimal places: 7.3224 ≈ 7.32 .
The total mass, reported to the appropriate number of significant figures, is 7.32 g .
Explanation
Understanding the Problem We are asked to find the total mass of two copper samples and report the result to the appropriate number of significant figures. The masses of the two samples are 1.6524 g and 5.67 g.
Adding the Masses To find the total mass, we need to add the two masses together: 1.6524 g + 5.67 g
Calculating the Sum Performing the addition, we get: 1.6524 + 5.67 = 7.3224
Significant Figures Now, we need to consider significant figures. The number 1.6524 has 5 significant figures, and the number 5.67 has 3 significant figures. When adding or subtracting numbers, the result should be rounded to the same number of decimal places as the number with the fewest decimal places. In this case, 5.67 has two decimal places, while 1.6524 has four decimal places. Therefore, we need to round our result to two decimal places.
Rounding the Result Rounding 7.3224 to two decimal places, we get 7.32.
Final Answer Therefore, the total mass of the two copper samples, reported to the appropriate number of significant figures, is 7.32 g.
Examples
Significant figures are important in many real-life situations, especially in science and engineering. For example, when measuring ingredients for a chemical reaction, the accuracy of the measurements affects the outcome of the reaction. Similarly, in construction, accurate measurements are crucial for ensuring the stability and safety of structures. By understanding significant figures, we can make more reliable and accurate measurements in various fields.
The total mass of the two copper samples, calculated and rounded to the appropriate number of significant figures, is 7.32 g. We arrived at this result by adding the two masses and rounding based on the least number of decimal places from the measurements. The significant figures guide us in ensuring the precision of our result is consistent with the measurements used.
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