Two masses of gold were measured before they were melted down. What is the total mass of the gold, reported to the appropriate number of significant figures?
$\begin{array}{r}
15.650 g \
+10.23 g \
\hline[?] g
\end{array}$
Answer (2)
The total mass of the gold is calculated by adding the two masses, resulting in 25.880 g. Since the least precise measurement is 10.23 g, we round the total to the hundredths place, giving us 25.88 g. Therefore, the final answer is 25.88 g, reported to the correct number of significant figures.
;
Add the two masses: 15.650 + 10.23 = 25.880 .
Identify the least precise measurement: 10.23 (hundredths place).
Round the sum to the hundredths place: 25.880 ≈ 25.88 .
The total mass of the gold is 25.88 g .
Explanation
Understanding the Problem We are given two masses of gold, 15.650 g and 10.23 g, and we need to find the total mass, reported to the appropriate number of significant figures.
Adding the Masses To find the total mass, we add the two masses together: 15.650 + 10.23 = 25.880
Significant Figures Now, we need to consider significant figures. The number 15.650 has 5 significant figures, and the number 10.23 has 4 significant figures. When adding or subtracting, the result should be rounded to the same number of decimal places as the least precise measurement. In this case, 10.23 is precise to the hundredths place (two decimal places), while 15.650 is precise to the thousandths place (three decimal places). Therefore, we need to round our answer to the hundredths place.
Rounding the Result Rounding 25.880 to the hundredths place gives us 25.88.
Final Answer Therefore, the total mass of the gold, reported to the appropriate number of significant figures, is 25.88 g.
Examples
When measuring ingredients for a recipe, it's crucial to consider significant figures to ensure accuracy. For instance, if you're adding 125.5 mL of water and 50.0 mL of vinegar, the least precise measurement (50.0 mL) has one decimal place. Therefore, the total volume should be reported as 175.5 mL, maintaining the same level of precision as the least precise measurement. This ensures that the final dish maintains the intended flavor and consistency.
