Rounding errors | Maths | Quizalize & Oak National Academy

Starter quiz

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

approximation

average

estimate

integer ✓
Round 384 to the nearest 10.

'380' ✓
Round 30.499999 to the nearest integer.

'30' ✓
Round 0.0002832 to 1 significant figure.

'0.0003' ✓
When a number is rounded to the nearest integer it is 4. Select the possible unrounded numbers.

4.238 ✓

3.90349 ✓

3.99843 ✓

3.099999

3.4999999
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.

'10' ✓

Exit quiz

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

Smallest integer = 675, largest integer = 684 ✓
State the smallest and largest integers that round to 500 when rounded to the nearest 20.

Smallest integer = 480, largest integer = 514

Smallest integer = 490, largest integer = 509 ✓

Smallest integer = 500, largest integer = 510

Smallest integer = 485, largest integer = 514

Smallest integer = 490, largest integer = 514
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

Smallest integer = 675, largest integer = 724 ✓

Smallest integer = 674, largest integer = 725
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.

'36 500' ✓
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 $^2$

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 $^2$

Lucas: $2.39\times5.78= 13.8142 = 13.8$ km $^2$ ✓
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

4.3 km² ✓

4.5 km²

Worksheet

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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.

Common misconception

Rounding prematurely during multi-step calculations.

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

Keywords

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