Measurement Math Example 1

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Example 1

easy
A ruler measures a pencil as 14.7 cm. The ruler has markings to the nearest 0.1 cm. Explain measurement error and determine the range of true values.

Solution

  1. 1
    The ruler reads 14.7 cm with precision to 0.1 cm
  2. 2
    Measurement error is at most half the precision unit: ±0.05\pm 0.05 cm
  3. 3
    True value range: 14.7−0.05≤true length≤14.7+0.0514.7 - 0.05 \leq \text{true length} \leq 14.7 + 0.05
  4. 4
    So the true length is between 14.65 cm and 14.75 cm

Answer

True length is in [14.65,14.75][14.65, 14.75] cm due to ±0.05\pm 0.05 cm measurement error.
All measurements have inherent error bounded by the instrument's precision. The reported value is the best estimate; the true value lies within half a precision unit on either side. Reporting appropriate significant figures communicates this uncertainty.

About Measurement

Measurement is the process of assigning numerical values to attributes of objects or events according to a defined rule or scale.

Learn more about Measurement →

More Measurement Examples

Example 2 medium

A scale consistently reads 0.5 kg too high (systematic error). A second scale gives variable reading

Example 3 easy

Five measurements of the same object yield: [formula] grams. Calculate the mean and comment on the p

Example 4 hard

A thermometer reads the boiling point of water as 99.2°C at sea level (true value: 100°C). If 10 rep

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