~ 4.13 ~

Measurement Error

Learning Targets

  • I understand that all measurements include some error.

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

Notes

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.

Vocabulary

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.

percent error: the error expressed as a percentage of the actual value measurement error ÷ actual value = % error.

Activities

13.2 Measuring a Soccer Field

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.

Add to Your Notes

When might percent error be more useful than measurement error?

    • If needed, give an example of measuring a student's height and being incorrect by an inch versus measuring the height of a skyscraper and being incorrect by an inch. Although the measurement error is the same (1 inch), the percent error is very different since the 1 inch difference is significantly more important when measuring shorter distances.

What is measurement error? What causes measurement error?

    • Measurement error is the difference between a measurement of an object and it’s actual measure. Human error can cause it, like when using a measuring tool wrong!

How can we minimize the amount of error?

    • Use accurate measuring tools and use them carefully.

What is the relationship between measurement error and percent error?

    • Percent error is the measurement error ÷ the actual number.

Summary

Summary is joined with 4.14 Percent Error.

Assignment

Check Google Classroom!