What is Rounding? — Mathematics

Definition 21.6 Primary & Middle School Mathematics · Chapter 21 — Large Numbers

To round a number to the nearest thousand (or ten, hundred, million …), replace it by the closest multiple of $1\,000$ . If the number sits exactly halfway, round up. In practice: look at the digit just below the rounding place — $5$ or more rounds up, $4$ or less rounds down.

Rounding 37\,614 to the nearest thousand: it lies past the halfway mark 37\,500, so it rounds up to 38\,000. — Rounding $37\,614$ to the nearest thousand: it lies past the halfway mark $37\,500$ , so it rounds up to $38\,000$ .

Examples

Example 21.7

$37\,614$ rounded to the nearest thousand: the hundreds digit is $6$ , so round up: $38\,000$ . Rounded to the nearest hundred: $37\,600$ . Rounded to the nearest ten thousand: $40\,000$ .

Example 21.8 (Orders of magnitude in the world)

Rounding is how large numbers are actually used: a country of $67\,842\,591$ inhabitants is “about $68$ million”; a city of $214\,376$ people is “about $200\,000$ ”. The exact figure changes every day anyway — the rounded one carries the useful information.

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Definition 29.7 Primary & Middle School Mathematics · Chapter 29 — Decimal Numbers

To round to the unit (or tenth, or hundredth), look at the next digit: $5$ or more rounds up, otherwise round down. So $4.362$ rounds to $4$ (unit), to $4.4$ (tenth), to $4.36$ (hundredth).

Examples

Example 29.8 (Money rounds to cents)

A price computed as $7.4983$ is displayed as $7.50$ : real-life amounts are rounded to the hundredth. Note the cascade: $7.4983 \to 7.50$ , where the $49$ became $50$ — rounding can ripple through several digits.

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Definition 38.9 Primary & Middle School Mathematics · Chapter 38 — Decimal Numbers

The rounding of a number to the unit (or tenth, hundredth, …) is the closest number with that precision. Look at the next digit: if it is $0,1,2,3,4$ , round down (keep); if it is $5,6,7,8,9$ , round up.

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