Year 6 Maths Decimals

Round decimals - to the nearest whole number

Q: Does 0.49 round to 0 or 1?

0, because its tenths digit is 4.

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Theory

To round a decimal to the nearest whole number, look only at the tenths digit. If it is $5$ or more, round up; if it is $4$ or less, keep the whole number. This Year 6 maths page shows the rule on a number line and uses rounding to estimate.

Rounding replaces a number with a nearby simpler number. To the nearest whole number, $8.4$ rounds to $8$ because it is closer to $8$ than to $9$.

Only the tenths digit (the first digit after the point) decides. $3.45$ rounds to $3$: its tenths digit is $4$, and the $5$ in the hundredths does not matter.

A number exactly halfway (tenths digit $5$, nothing after) rounds up: $6.5$ rounds to $7$.

Rounding up can change more than one digit: $19.7$ rounds to $20$.

$4.7$ is past $4.5$, so it is closer to $5$: $4.7 \to 5$.

$12.62$ has tenths digit $6$: it rounds up to $13$.

The rule:

\[ \text{tenths } 0\text{-}4 \Rightarrow \text{keep} \]

tenths digit 0 to 4 keep

\[ \text{tenths } 5\text{-}9 \Rightarrow \text{round up} \]

tenths digit 5 to 9 round up

          Look at one digit only. For \(3.45\), the tenths digit is \(4\), so it rounds to \(3\), not \(4\).
        

Halfway goes up. $6.5 \to 7$.

Rounding to the nearest whole number

Find the tenths digit.
If it is 5 or more, add $1$ to the whole number part.
If it is 4 or less, keep the whole number part.
Drop the decimal part.

Example 1 — Round down

Round $8.4$ to the nearest whole number.

Solution

Tenths digit $4$: $8$.

Example 2 — Round up

Round $12.62$ to the nearest whole number.

Solution

Tenths digit $6$: $13$.

Example 3 — Halfway

Round $6.5$ to the nearest whole number.

Solution

Exactly halfway, so round up: $7$.

Example 4 — Several at once

Round each to the nearest whole number.
(i) $0.49$
(ii) $19.7$
(iii) $27.09$

Solution

(i) $0$
(ii) $20$
(iii) $27$

Example 5 — Only the tenths

Round $3.45$ to the nearest whole number.

Solution

Tenths digit $4$, so $3$. Do not round the $5$ first.

Example 6 — Estimate a total

Prices are $\$7.80$, $\$2.35$ and $\$11.60$.
(i) Round each to the nearest dollar.
(ii) Estimate the total.

Solution

$8 + 2 + 12$

$=$

$22$

8 + 2 + 12 = 22

(i) $\$8$, $\$2$, $\$12$
(ii) About $\$22$ (the exact total is $\$21.75$)

Example 7 — Measurement

A bag of sand has a mass of $4.7$ kg. What is that to the nearest kilogram?

Solution

$5$ kg (see the first diagram).

Example 8 — Find the mistake

Kai rounded $5.48$ to $6$ by rounding $5.48$ to $5.5$ first. What is right?

Solution

Round in one step using the tenths digit ($4$): $5.48$ rounds to $5$.

Common pitfalls

Rounding in steps. Rounding twice can give the wrong answer. Use the tenths digit once.

Looking at the last digit. Only the tenths digit matters for the nearest whole number.

Forgetting to carry. $19.7$ rounds to $20$, not $19$ or $10$.

Leaving the decimal part. The rounded answer is a whole number: $13$, not $13.62$.

Frequently asked questions

Which digit decides when rounding to a whole number?

The tenths digit.

What happens to a number ending in .5?

It rounds up: $6.5 \to 7$.

Does 0.49 round to 0 or 1?

$0$, because its tenths digit is $4$.

Why round prices?

To estimate a total quickly.

What is 19.7 to the nearest whole number?

$20$.

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Round decimals - to 1 decimal place

Round decimals - to the nearest whole number

📖 Theory

Rounding to the nearest whole number

Common pitfalls

Frequently asked questions

Theory