Rounding numbers

What is rounding a number

Rounding is replacing a number with the nearest "round" value. For example, the number 47 can be rounded to 50, and the number 123 — to 120 or 100, depending on the place value you are rounding to.

Rounding is denoted by the sign ≈ (approximately equal to). For example: 47 ≈ 50.

Rules for rounding numbers

To round a number to a specified place value, you need to:

underline the digit of that place value;
look at the next digit to its right;
if this digit is 0, 1, 2, 3, or 4 — leave the underlined digit unchanged; if it is 5, 6, 7, 8, or 9 — increase it by 1.

All digits after the rounded place value are replaced by zeros (for whole numbers) or dropped (for fractions).

Rounding to tens

To round a number to tens, look at the ones digit.

Example:

124 ≈ 120 — ones digit 4, leave the tens digit 2 unchanged;
147 ≈ 150 — ones digit 7, increase the tens digit 4 by 1.

Rounding to hundreds

To round to hundreds, look at the tens digit.

Example:

134 ≈ 100 — tens digit 3, leave the hundreds digit 1 unchanged;
256 ≈ 300 — tens digit 5, increase the hundreds digit 2 by 1.

Rounding to thousands

To round to thousands, look at the hundreds digit: 1234 ≈ 1000 (hundreds digit 2); 1750 ≈ 2000 (hundreds digit 7).

Rounding decimals

Decimals are rounded to tenths, hundredths, thousandths, etc. The rule is the same: look at the next digit and increase or leave unchanged.

3.14159 ≈ 3.14 (to hundredths); 2.718 ≈ 2.72 (to hundredths); 0.6666 ≈ 0.67 (to hundredths).

Absolute and relative rounding error

The absolute rounding error is the modulus of the difference between the exact and approximate value. The relative error is the ratio of the absolute error to the exact value, usually expressed as a percentage.

Estimation and evaluation of results

Rounding helps to quickly estimate the result of calculations. For example, to quickly estimate 19 × 21, you can replace the factors with 20 × 20 = 400 — the exact answer is 399.

Rounding in grades 5 and 6

In grade 5, natural numbers are rounded; in grade 6, decimals are added. In grade 9, rounding is used when evaluating calculation results in the OGE and when solving physics problems.

Main topics in grade 5: rounding to tens, hundreds, thousands; in grade 6: rounding to tenths, hundredths, thousandths.

Frequently asked questions

How do you round a number to tens?

Look at the ones digit: if it is 0–4, the tens digit does not change; if it is 5–9, the tens digit is increased by 1 and the ones are replaced by zero. For example: 43 ≈ 40, 47 ≈ 50.

What if the digit after the rounded digit is 5?

According to the standard rounding rule, if the digit after the rounded digit is 5, the rounded digit is increased by 1. For example: 2.5 ≈ 3.

What is the difference between rounding down and rounding up?

Rounding down means the resulting number is smaller than the original. Rounding up means the resulting number is greater than the original. For example, 47 ≈ 40 — rounded down; 47 ≈ 50 — rounded up.

In what grade is rounding studied?

In grade 5 — rounding of natural numbers; in grade 6 — rounding of decimals; in grade 9 — estimation and evaluation of results, rounding error.