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Year 8

Rounding errors

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.

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New
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Year 8

Rounding errors

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.

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Lesson details

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.

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.
Teacher tip

Equipment

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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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

Exit quiz

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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