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All courses Algebra I · N-Q.3 36 of 76
Report quantities with accuracy appropriate to measurement limitations.

Round a measurement result to the correct decimal place

Problem
Compute \(12.4~\text{cm}~+~8.7~\text{cm}\). Round the result to the nearest tenth of a centimeter because the measurements were recorded to that precision.
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
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Hint

Add the two decimal measurements first, then check whether the sum already has one decimal place.

If measurements are recorded to the nearest tenth, report the result to one decimal place.

Solution walkthrough

01

Identify the reporting precision

\[\text{nearest}~\text{tenth}~=~1~\text{decimal}~\text{place}\]

Both measurements were recorded to the nearest tenth of a centimeter, and the prompt explicitly requires the sum at that same precision. The final measurement must therefore contain one decimal place.

02

Align and add the measurements

\[12.4~\text{cm}~+~8.7~\text{cm}~=~21.1~\text{cm}\]

Add centimeters to centimeters and align the decimal points. Four tenths plus seven tenths is eleven tenths, producing a carry of 1 whole centimeter and leaving 1 tenth; the total is 21.1 centimeters.

03

Check the magnitude and decimal place

\[12~+~9~=~21;~21.1~\text{has}~1~\text{decimal}~\text{place}\]

The estimate 12 plus 9 is 21, so 21.1 is a reasonable exact sum. It already has the required one decimal place, so rounding to the nearest tenth does not change it.

04

Report the measured sum

\[21.1~\text{cm}\]

The appropriately rounded result is 21.1 centimeters, exactly matching choice A.

+

Another way

  1. Add tenths as whole numbers: 124 tenths + 87 tenths = 211 tenths = 21.1 centimeters.

!

Common mistake

Do not write 21 cm. Dropping the tenths digit reports less precision than the prompt requires and discards measurement information supported by both inputs.

Solution walkthrough video