The masses of two samples were measured. What is the total mass, reported to the appropriate number of significant figures?
[tex]$24.964 g + 0.7643 g = [?] g$[/tex]
Answer (2)
Add the two masses: 24.964 g + 0.7643 g = 25.7283 g .
Identify the least number of decimal places: 3 (from 24.964).
Round the result to 3 decimal places: 25.728 g .
The total mass reported to the appropriate number of significant figures is 25.728 g .
Explanation
Problem Analysis We are asked to find the total mass of two samples and report the result to the appropriate number of significant figures. The given masses are 24.964 g and 0.7643 g .
Adding the Masses To find the total mass, we add the two masses together: 24.964 g + 0.7643 g = 25.7283 g
Significant Figures Rule Now, we need to consider significant figures. When adding or subtracting, the result should have the same number of decimal places as the number with the fewest decimal places. In this case, 24.964 has three decimal places, and 0.7643 has four decimal places. Therefore, our answer should have three decimal places.
Rounding the Result Rounding 25.7283 to three decimal places, we get 25.728 .
Final Answer Therefore, the total mass, reported to the appropriate number of significant figures, is 25.728 g .
Examples
In a chemistry lab, you might need to add two chemicals together. One chemical weighs 24.964 grams, and the other weighs 0.7643 grams. To accurately measure the total weight for your experiment, you must add these values and round to the correct number of decimal places based on the least precise measurement. This ensures your calculations and experiment results are as accurate as possible.
The total mass of the two samples is calculated by adding them to get 25.7283 g and rounding to the appropriate number of significant figures, which is 25.728 g. This rounding is necessary because the mass with the least precision dictates the level of accuracy in the result. Therefore, the total mass reported is 25.728 g.
;
