Percent error

About this lesson

Algebra I › Relationships between quantities

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Percent error

Warm-up

Three quick questions from earlier lessons.

Discover

A 50 cm board is measured as 52 cm. Which describes the error?

  1. A 4% error
  2. A 2% error

Key idea

Percent error compares the error with the actual value.

Percent error =∣measured−actual∣actual×100= \dfrac{|\text{measured} - \text{actual}|}{\text{actual}} \times 100. A tolerance of p%p\% allows values within p%p\% of the target, above or below.

Worked example

A 400 g bag with at most 5% error.

2020 g
5% of 400.
From 380 g to 420 g
Range.

Your turn, guided

Your turn: actual 40, measured 38. The percent error.

55
2 ÷ 40 × 100.

Practice ★

  1. A board is really 36 cm long, but Ana measures 40 cm. What is her percent error?
  2. A board is really 73 cm long, but Ana measures 76 cm. What is her percent error?
  1. A box really holds 400 cups, but a label says 520. What is the percent error?

Watch out!

Practice ★★

  1. A bag should hold 600 g of rice, with at most 7% error. What is the smallest allowed mass (g)?
  2. A bag should hold 400 g of rice, with at most 8% error. What is the smallest allowed mass (g)?

Exit ticket

Three questions to check you have got it.

  1. A board is really 36 cm long, but Ana measures 40 cm. What is her percent error?
  2. A board is really 73 cm long, but Ana measures 76 cm. What is her percent error?
  3. A board is really 52 cm long, but Ana measures 53 cm. What is her percent error?

Summary card

Percent error

Error ÷ actual × 100.

Watch out: divide by the actual value, not the measured one.

End of the lesson

Back to the chapter

Answers: Percent error

A

  1. 1009\frac{100}{9}
  2. 30073\frac{300}{73}

B

  1. 3030

C

  1. 558558
  2. 368368

D

  1. 1009\frac{100}{9}
  2. 30073\frac{300}{73}
  3. 2513\frac{25}{13}

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