Add or subtract the following measurements. Be sure each answer you enter contains the correct number
[tex]
\begin{aligned}
14.500 g-0.70 g & =\square g \\
11.570 g-0.8 g & =\square g \\
15.5 g+1.320 g & =\square g
\end{aligned}
[/tex]
Answer (1)
Subtract 0.70 from 14.500, round the result to two decimal places: 14.500 − 0.70 = 13.80 g .
Subtract 0.8 from 11.570, round the result to one decimal place: 11.570 − 0.8 = 10.8 g .
Add 15.5 and 1.320, round the result to one decimal place: 15.5 + 1.320 = 16.8 g .
The results, considering significant figures, are: 13.80 g , 10.8 g , 16.8 g .
Explanation
Understanding the Problem We need to perform addition and subtraction of measurements, adhering to significant figures rules. When adding or subtracting, the result should have the same number of decimal places as the measurement with the fewest decimal places.
Calculating the First Subtraction First, we calculate 14.500 g − 0.70 g . The result of the subtraction is 13.8 . The measurement 0.70 g has two decimal places, so the answer should have two decimal places. Therefore, the answer is 13.80 g .
Calculating the Second Subtraction Next, we calculate 11.570 g − 0.8 g . The result of the subtraction is 10.77 . The measurement 0.8 g has one decimal place, so the answer should have one decimal place. Therefore, the answer is 10.8 g .
Calculating the Addition Finally, we calculate 15.5 g + 1.320 g . The result of the addition is 16.82 . The measurement 15.5 g has one decimal place, so the answer should have one decimal place. Therefore, the answer is 16.8 g .
Final Answer Therefore, the answers are:
14.500 g − 0.70 g = 13.80 g
11.570 g − 0.8 g = 10.8 g
15.5 g + 1.320 g = 16.8 g
Examples
In a laboratory setting, precise measurements are crucial for accurate results. When combining chemicals, scientists must consider significant figures to ensure the final mixture has the correct concentration. For example, if a chemist adds 15.5 g of a substance to 1.320 g of another, the final mass must be reported as 16.8 g, reflecting the least precise measurement. This attention to detail prevents errors and maintains the integrity of experiments, highlighting the practical importance of significant figures in scientific measurements.
