Rounding replaces a number with a nearby number that is easier to work with. The answer is less exact on purpose. What matters is that the replacement is the closest number at the level of accuracy you asked for.
The procedure
- Underline the digit in the place you are rounding to.
- Look at the single digit immediately to its right.
- If that digit is 5 or more, the underlined digit goes up by one. If it is 4 or less, the underlined digit stays.
- Every digit to the right becomes zero, or for decimals, is dropped.
Only one digit decides
Rounding 4,449 to the nearest hundred, the tens digit is 4, so the answer is 4,400. The 9 in the ones place is not allowed a vote. Rounding twice, first to 4,450 and then to 4,500, is a real and common error with a name: double rounding.
One number, four different roundings
47,382 nearest ten 47,380 nearest hundred 47,400 nearest thousand 47,000 nearest ten thousand 50,000
Rounding decimals
Rounding 3.8471
nearest tenth 3.8 nearest hundredth 3.85 nearest thousandth 3.847
For the hundredth, the digit to the right is 7, so the 4 goes up to 5.
When rounding up carries
Rounding 1,972 to the nearest hundred makes the hundreds digit 9 go up, which turns it into ten hundreds. That carries into the thousands: the answer is 2,000. This is not a special case, it is ordinary carrying.
Rounding outside the classroom
Rounding is not only an exercise. Almost every large number quoted in public has been rounded, and knowing to what place matters when the numbers are compared.
- Shopping. Rounding each price to the nearest dollar keeps a running total close enough to know whether the money will stretch.
- Populations. A city described as having 400,000 people has been rounded to the nearest ten thousand at least. Treating that figure as exact and subtracting another rounded figure gives a difference far less precise than it looks.
- Measurement. A length reported as 3.5 metres usually means somewhere between 3.45 and 3.55, so a calculation built on it cannot be more precise than that.
The general point: an answer cannot be more accurate than the numbers that went into it, and rounding early in a long calculation makes the final answer worse than rounding once at the end.
Common mistakes
Rounding in stages
Round once, from the original number, to the place you were asked for.
Leaving the trailing digits alone
Rounding 47,382 to the nearest thousand gives 47,000, not 47,382 with a note. The digits to the right of the rounding place must become zeros.
Check yourself
Round 6,548 to the nearest hundred.
6,500. The tens digit is 4, so the hundreds digit stays.
Round 6,548 to the nearest thousand.
7,000. The hundreds digit is 5, so the thousands digit goes up.
Round 0.0649 to the nearest hundredth.
0.06. The digit to the right of the hundredths place is 4.
Round 3,996 to the nearest ten.
4,000. Rounding the tens digit up carries through the hundreds and the thousands.
See also
Sources
- Standard rounding conventions used in United States elementary mathematics, where a digit of five rounds the place up. Examples on this page are our own.