~ 4.13 ~

Learning Targets

• I understand that all measurements include some error.

• I can represent measurement error as a percentage of the correct measurement.

When we are measuring a length using a ruler or measuring tape, we can get a measurement that is different from the actual length. This could be because we positioned the ruler incorrectly, or it could be because the ruler is not very precise. There is always at least a small difference between the actual length and a measured length, even if it is a microscopic difference!

Here are two rulers with different markings.

The second ruler is marked in millimeters, so it is easier to get a measurement to the nearest tenth of a centimeter with this ruler than with the first. For example, a line that is actually 6.2 cm long might be measured to be 6 cm long by the first ruler, because we measure to the nearest centimeter.

The measurement error is the positive difference between the measurement and the actual value. Measurement error is often expressed as a percentage of the actual value. We always use a positive number to express measurement error and, when appropriate, use words to describe whether the measurement is greater than or less than the actual value.

For example, if we get 6 cm when we measure a line that is actually 6.2 cm long, then the measurement error is 0.2 cm, or about 3.2%, because 0.2 ÷ 6.2 ≈ 0.032.

Measurement error can result from the precision level of your measuring device.

measurement error: Measurement error is the positive difference between a measurement of a quantity and the actual quantity. It is often expressed as a percentage of the actual value. For example, if we get 6 cm when we measure a line that is actually 6.2 cm long, then the measurement error is 0.2 cm and the percent error is 3.2%, because 0.2 ÷ 6.2 = 0.032.

A soccer field is 120 yards long. Han measures the length of the field using a 30-foot-long tape measure and gets a measurement of 358 feet, 10 inches.

• 1. What is the amount of the error?

  2. Express the error as a percentage of the actual length of the field.

What is the possible cause of the error in the Soccer Field problem?

• • He did not position the tape measure precisely every time he measured another 30 feet.

  • He didn’t go in a completely straight line.

  • Han did not correctly use the measuring tape.

Summary is joined with 4.14 Percent Error.

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