POP

G1.7 Rounding to Decimal Places and Significant Figures

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01 — Explanation

How is rounding to a decimal place different from rounding to a whole number?

The method is identical to rounding whole numbers — find the rounding digit, check the deciding digit to its right, and round up or down — but now the rounding digit sits after the decimal point, so the digits beyond it are simply dropped rather than turned into zeros.

Example: Round 18.7 to the nearest whole number.

The rounding digit is $8$ (units place); the deciding digit is $7$ (tenths place).
Since $7 \geq 5$ , round up: $8 \to 9$ , and the decimal part is dropped entirely.
The answer is $19$ .

Example: Round 2.456 to two decimal places.

The rounding digit is $5$ (hundredths place); the deciding digit is $6$ (thousandths place).
Since $6 \geq 5$ , round up: $5 \to 6$ .
The answer is $2.46$ .

Common Mistake

When rounding up causes a "9" to roll over, forgetting to carry into the next column — e.g. rounding $2.996$ to 2 decimal places: the deciding digit (the final 6) rounds the 9 up, which rolls $0.99 \to 1.00$ , giving $3.00$ , not $2.00$ or $2.99$ . Always carry a rounding "carry" the same way you would in addition.

02 — Explanation

What are significant figures, and how do I count them?

The first significant figure of a number is its first non-zero digit, reading from the left; every digit after that counts as significant too (including zeros between non-zero digits, and trailing zeros after a decimal point). Leading zeros (like the $0$ in $0.0034$ ) are never significant — they're just placeholders.

03 — Explanation

How do I round to a given number of significant figures?

Count to the significant figure you're rounding to, then apply the same deciding-digit rule as before. For a whole number, any digits dropped to the right become zeros (to preserve the number's size); for a decimal, they're simply dropped.

Example: Round 4321 to 1 significant figure.

The first significant figure is $4$ ; the deciding digit is $3$ .
Since $3 < 5$ , round down: the $4$ stays, and the rest become zeros.
The answer is $4000$ .

Example: Round 0.03847 to 2 significant figures.

The first significant figure is $3$ (the leading zeros don't count), so the second significant figure is $8$ ; the deciding digit is $4$ .
Since $4 < 5$ , round down: $0.038$ .

Exam Tip

A very common instruction is "round to 3 significant figures" on an answer involving a large whole number, e.g. rounding $52{,}847$ to 3 s.f. The first three significant figures are $5$ , $2$ , $8$ — but you must still write the answer as $52{,}800$ (keeping the place value correct with trailing zeros), not just "528".

04 — Worked example

Worked Exam-Style Question

A calculation gives an answer of $0.0069284$ . Round this answer to (a) 2 decimal places and (b) 3 significant figures.

(a) To 2 decimal places, the rounding digit is the second digit after the point, which is $0$ ; the deciding digit (third place) is $6$ . Since $6 \geq 5$ , round up: $0.00 \to 0.01$ .
(b) The first significant figure is $6$ (first non-zero digit), so the third significant figure is $2$ ; the deciding digit is $8$ . Since $8 \geq 5$ , round up: $0.00693$ .

Exam Tip

Decimal places and significant figures count from different starting points — decimal places always count from the decimal point, while significant figures start from the first non-zero digit. Always re-read which one the question is actually asking for before you round.