Precision Math Example 2

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Example 2

hard
Add 12.312.3 cm and 4.564.56 cm, applying the rule for precision in addition.

Solution

  1. 1
    Identify the precision of each: 12.312.3 cm is precise to the tenths place (1 decimal place); 4.564.56 cm is precise to the hundredths place (2 decimal places).
  2. 2
    In addition, the result can be no more precise than the least precise input: tenths place.
  3. 3
    Sum: 12.3+4.56=16.8612.3 + 4.56 = 16.86 cm. Round to tenths: 16.916.9 cm.

Answer

12.3+4.56=16.912.3 + 4.56 = 16.9 cm (to the tenths place).
When adding or subtracting measured quantities, the result is limited to the precision of the least precise measurement. This is because the uncertain digit propagates — you cannot know the tenths from 12.312.3 precisely, so the hundredths in the sum are also uncertain.

About Precision

The degree of exactness in a measurement or calculation, reflected in the number of significant digits reported.

Learn more about Precision →

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