Two masses of carbon were combined in a flask. What is the total mass of carbon, reported to the appropriate number of significant figures?
[tex]
\begin{array}{r}
8.2 g \
+0.6634 g \
\hline[?] g
\end{array}
[/tex]
Answer (2)
The total mass of carbon from the two measurements is calculated by adding 8.2 g and 0.6634 g, resulting in 8.8634 g. This value is rounded to the nearest one decimal place due to the significant figures, yielding a total of 8.9 g. Therefore, the final answer is 8.9 g.
;
Add the two masses: 8.2 + 0.6634 = 8.8634 .
Identify the least precise measurement: 8.2 g (two significant figures, one decimal place).
Round the sum to one decimal place: 8.9 .
The total mass of carbon is 8.9 g.
Explanation
Understanding the Problem We are asked to add two masses of carbon and report the total mass to the appropriate number of significant figures. The given masses are 8.2 g and 0.6634 g.
Adding the Masses First, we add the two masses: 8.2 g + 0.6634 g = 8.8634 g
Significant Figures Next, we need to consider significant figures. The number 8.2 has two significant figures, while 0.6634 has four significant figures. When adding or subtracting, the result should be rounded to the same number of decimal places as the number with the fewest decimal places. In this case, 8.2 has one decimal place, and 0.6634 has four decimal places. Therefore, we should round our answer to one decimal place.
Rounding the Result Rounding 8.8634 g to one decimal place gives us 8.9 g.
Final Answer Therefore, the total mass of carbon, reported to the appropriate number of significant figures, is 8.9 g.
Examples
Significant figures are important in many real-life applications, especially in science and engineering. For example, when measuring ingredients for a chemical reaction, the accuracy of the measurement is limited by the measuring device. If you are using a scale that only measures to the nearest gram, you cannot accurately measure to the nearest milligram. Therefore, you must report your results to the correct number of significant figures to avoid overstating the accuracy of your measurement. This ensures that calculations based on these measurements reflect the true precision of the experiment or process.
