Add or subtract the following measurements. Be sure each answer you enter contains the correct number of significant digits.
[tex]
\begin{aligned}
14.6 mL+15.50 mL & =\square mL \\
15.61 mL-5.5 mL & =\square mL \\
3.520 mL+18.8 mL & =\square mL
\end{aligned}
[/tex]
Answer (2)
Add 14.6 m L + 15.50 m L . Round the result 30.10 m L to one decimal place: 30.1 m L .
Subtract 15.61 m L − 5.5 m L . Round the result 10.11 m L to one decimal place: 10.1 m L .
Add 3.520 m L + 18.8 m L . Round the result 22.320 m L to one decimal place: 22.3 m L .
The final answers are: 30.1 m L , 10.1 m L , and 22.3 m L . 30.1 m L , 10.1 m L , 22.3 m L
Explanation
Understanding Significant Figures We need to perform addition and subtraction of measurements, paying close attention to significant figures. The rule for addition and subtraction is that the result should have the same number of decimal places as the measurement with the fewest decimal places.
Adding the First Pair of Measurements Let's perform the first addition: 14.6 m L + 15.50 m L . The number 14.6 has one decimal place, and 15.50 has two decimal places. Therefore, the result should have one decimal place. The sum is 14.6 + 15.50 = 30.10 . Rounding to one decimal place, we get 30.1 m L .
Subtracting the Second Pair of Measurements Next, let's perform the subtraction: 15.61 m L − 5.5 m L . The number 15.61 has two decimal places, and 5.5 has one decimal place. Therefore, the result should have one decimal place. The difference is 15.61 − 5.5 = 10.11 . Rounding to one decimal place, we get 10.1 m L .
Adding the Third Pair of Measurements Finally, let's perform the second addition: 3.520 m L + 18.8 m L . The number 3.520 has three decimal places, and 18.8 has one decimal place. Therefore, the result should have one decimal place. The sum is 3.520 + 18.8 = 22.320 . Rounding to one decimal place, we get 22.3 m L .
Final Answer Therefore, the answers are:
14.6 m L + 15.50 m L = 30.1 m L 15.61 m L − 5.5 m L = 10.1 m L 3.520 m L + 18.8 m L = 22.3 m L
Examples
In a chemistry lab, you might need to add precise volumes of liquids. If you're using a graduated cylinder that measures to the nearest tenth of a milliliter (0.1 mL) and another that measures to the nearest hundredth of a milliliter (0.01 mL), when you combine them, your final measurement can only be as precise as the least precise measurement. This ensures that your calculations and experiments remain accurate and reliable, preventing errors that could arise from overstating the precision of your measurements. For example, mixing 14.6 mL of a solution with 15.50 mL of another solution would result in a total volume reported as 30.1 mL, reflecting the precision of the 14.6 mL measurement.
The calculations provide the following results: 14.6 m L + 15.50 m L = 30.1 m L , 15.61 m L − 5.5 m L = 10.1 m L , and 3.520 m L + 18.8 m L = 22.3 m L , all rounded to the correct number of significant figures.
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