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      Lesson details

      Learning outcome

      I can appreciate the impact of rounding errors when using a calculator (or other technology), and the way that these can be compounded to result in large inaccuracies.

      Key learning points

      1. When given a rounded number you can say what the biggest and smallest values of the unrounded number could have been.
      2. When using technology for multi-step calculations you might round along the way.
      3. Rounding too early can cause answers to be incorrect
      4. Repeated rounding in multi-step calculations can lead to large errors.

      Keywords

      • Significant figures - Significant figures are the digits in a number that contribute to the accuracy of the number

      Common misconception

      Rounding prematurely during multi-step calculations.

      Encourage to use of fractions (where possible) or the use of the ANS button.

      Teacher tip

      A quire fire of questions where pupils need to draw number lines to show the range of integers on MWB will aid pupils when finding unrounded numbers when given a degree of accuracy. This helps the visualization of finding unrounded intervals. eg. Show 90 rounded to the nearest 10.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      An __________ is any positive or negative whole number and zero.

      approximation
      average
      estimate
      Correct answer: integer

      Q2.
      Round 384 to the nearest 10.

      Correct Answer: 380

      Q3.
      Round 30.499999 to the nearest integer.

      Correct Answer: 30

      Q4.
      Round 0.0002832 to 1 significant figure.

      Correct Answer: 0.0003

      Q5.
      When a number is rounded to the nearest integer it is 4. Select the possible unrounded numbers.

      Correct answer: 4.238
      Correct answer: 3.90349
      Correct answer: 3.99843
      3.099999
      3.4999999

      Q6.
      Round each number in the calculation to 1 significant figure and calculate the answer. $$\frac{89.7+9.58}{5.34+4.58}$$. Give your answer as an integer.

      Correct Answer: 10, ten

      6 Questions

      Q1.
      State the smallest and largest integers that round to 680 when rounded to the nearest 10.

      Smallest integer = 674, largest integer = 684
      Smallest integer = 670, largest integer = 680
      Smallest integer = 670, largest integer = 690
      Correct answer: Smallest integer = 675, largest integer = 684

      Q2.
      State the smallest and largest integers that round to 500 when rounded to the nearest 20.

      Smallest integer = 480, largest integer = 514
      Correct answer: Smallest integer = 490, largest integer = 509
      Smallest integer = 500, largest integer = 510
      Smallest integer = 485, largest integer = 514
      Smallest integer = 490, largest integer = 514

      Q3.
      State the smallest and largest integers that round to 700 when rounded to the nearest 50.

      Smallest integer = 675, largest integer = 725
      Smallest integer = 674 largest integer = 724
      Smallest integer = 725, largest integer = 734
      Correct answer: Smallest integer = 675, largest integer = 724
      Smallest integer = 674, largest integer = 725

      Q4.
      An advert for a magazine says 37 000 people buy the magazine rounded to the nearest 1000. The fewest people who buy the magazine is people.

      Correct Answer: 36 500

      Q5.
      A plot of rectangular land measure 2.39 km (1 d.p.) by 5.78 km (1 d.p.). Five pupils work out the area of the plot of land. Whose working out and answer shows the most accurate answer to 1 d.p?

      Andeep: $$2.39\times5.78=2.4\times5.8=13.9$$ km$$^2$$
      Correct answer: Laura: $$2.39\times5.78= 13.814... = 13.8$$ km$$^2$$
      Sofia: $$2\times6= 12.0$$ km$$^2$$
      Jun: $$2.39\times5.78= 13.8142 = 13.9$$ km$$^2$$
      Correct answer: Lucas: $$2.39\times5.78= 13.8142 = 13.8$$ km$$^2$$

      Q6.
      A large plot of land has an area of 20 km². A small, rectangular lake with lengths 3.254 km by 4.814 km is planned, leaving the rest of the land as grass. Work out the area of grass to 1 d.p.

      3.3 km²
      4.1 km²
      Correct answer: 4.3 km²
      4.5 km²

      To help you plan your 8 maths lesson on: Rounding errors, download all teaching resources for free and adapt to suit your pupils' needs...