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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 13 of 16

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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

When given a rounded number you can say what the biggest and smallest values of the unrounded number could have been.
When using technology for multi-step calculations you might round along the way.
Rounding too early can cause answers to be incorrect
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.

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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).

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Prior knowledge 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

Assessment 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

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UnitMaths / Estimation and rounding

Maths

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Rounding errors

Rounding errors

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

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

Q2.Round 384 to the nearest 10.

Q3.Round 30.499999 to the nearest integer.

Q4.Round 0.0002832 to 1 significant figure.

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

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.

Assessment exit quiz

6 Questions

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

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

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

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.

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?

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.

Lesson appears in

UnitMaths / Estimation and rounding

Maths

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

Q2.
Round 384 to the nearest 10.

Q3.
Round 30.499999 to the nearest integer.

Q4.
Round 0.0002832 to 1 significant figure.

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

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.

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

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

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

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.

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?

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.