Rounding

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Rounding Numbers

Whole numbers • Tens • Decimal places • Significant figures

We round numbers to make them simpler while keeping them close to the original value.

In all methods we look at the next digit: if it is 0–4 we round down, if it is 5–9 we round up.

1 Nearest whole number
2 Nearest 10 (and other place values)
3 Decimal places
4 Significant figures

Examples of Rounding

Nearest Whole Number

3.2 ≈ 3

4.7 ≈ 5

5.5 ≈ 6

Nearest 10

34 ≈ 30

68 ≈ 70

145 ≈ 150

Decimal Places

3.746 ≈ 3.75 (2 d.p.)

9.803 ≈ 9.8 (1 d.p.)

12.995 ≈ 13.00 (2 d.p.)

Significant Figures

3476 ≈ 3500 (2 s.f.)

0.0379 ≈ 0.038 (2 s.f.)

1.999 ≈ 2.00 (3 s.f.)

Rounding Numbers

(A) Round each of the following numbers to the nearest 10:
(i) 137 (ii) 84 (iii) 677 (iv) 1764

(B) Round off these numbers to the nearest 100:
(i) 823 (ii) 276 (iii) 2184

Show worked solution

To the nearest 10:

(i) 137 → 140 (7 ≥ 5 → round up)

(ii) 84 → 80 (4 < 5 → round down)

(iii) 677 → 680 (7 ≥ 5 → round up)

(iv) 1764 → 1760 (4 < 5 → round down)

To the nearest 100:

(i) 823 → 800 (tens digit 2 < 5 → round down)

(ii) 276 → 300 (tens digit 7 ≥ 5 → round up)

(iii) 2184 → 2200 (tens digit 8 ≥ 5 → round up)

Rounding Interactive Simulation

00.0000

Significant Figures

Round \(28\,460\):
(i) to three significant figures
(ii) to two significant figures
(iii) to one significant figure.

Show worked solution

(i) Three significant figures

The first three significant digits are 2, 8 and 4 in \(28\,460\).

Look at the next digit (6). Since \(6 \ge 5\), round the 4 up to 5.

\(28\,460 \approx 28\,500\) (3 s.f.).

(ii) Two significant figures

The first two significant digits are 2 and 8.

The next digit is 4 (in the hundreds place). Since \(4 < 5\), leave the 8 as it is.

\(28\,460 \approx 28\,000\) (2 s.f.).

(iii) One significant figure

The first significant digit is 2 (in the ten-thousands place).

The next digit is 8. Since \(8 \ge 5\), round the 2 up to 3.

\(28\,460 \approx 30\,000\) (1 s.f.).

Rounding Quiz

Question 1 of 5 Score: 0 / 5

OnlineMaths.org Quiz Sample

Can you get three in a row to light up green?