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?
[tex]
\begin{array}{r}
15.650 g \\
+10.23 g \\
\hline \square g
\end{array}
[/tex]
Answer (2)
Add the two masses: 15.650 + 10.23 = 25.880 .
Identify the least precise decimal place: hundredths place.
Round the result to the hundredths place: 25.880 ≈ 25.88 .
The total mass of the gold is 25.88 g.
Explanation
Problem Analysis 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 given masses: 15.650 g + 10.23 g
Calculating the Sum Performing the addition, we get: 15.650 + 10.23 = 25.880
Significant Figures Analysis Now, we need to consider significant figures. The number 15.650 has five significant figures and is precise to the thousandths place. The number 10.23 has four significant figures and is precise to the hundredths place. When adding or subtracting, the result should be rounded to the least precise decimal place of the numbers being added. In this case, the least precise decimal place is the hundredths place.
Rounding to Correct Significant Figures Therefore, we round the result 25.880 to the hundredths place, which gives us 25.88.
Final Answer The total mass of the gold, reported to the appropriate number of significant figures, is 25.88 g.
Examples
In a laboratory setting, when combining different amounts of chemicals or substances, it's crucial to accurately determine the total mass. For example, if you're mixing two gold samples for an experiment, knowing the precise total mass (with correct significant figures) ensures the accuracy and reliability of your results. This is also applicable in cooking, where combining ingredients requires precise measurements to achieve the desired outcome. In construction, mixing cement or other materials also requires precise measurements to ensure the structural integrity of the building.
The total mass of the gold is calculated by adding the two masses, resulting in 25.880 g. Considering significant figures, we round this to 25.88 g since the least precise measurement is to the hundredths place. Therefore, the total mass of the gold, reported correctly, is 25.88 g.
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