Rounding calculator

To round a number means to replace it with the nearest “round” number of the chosen place value. The digit one place lower decides: 0 to 4 rounds down, 5 to 9 rounds up. The price £3,456.79 to the nearest hundred is about £3,500, because the digit in the tens place is a five.

Negative numbers are rounded in the same way as positive ones, and the minus sign is simply kept: −2.5 rounded to the nearest unit is −3.

How it works

The calculator uses the formula

$$y=\mathrm{round}\left(\frac{x}{r}\right)\cdot r$$

where r is the place value we round to: 100 for hundreds, or 0.01 for hundredths.

We round 3,456.789 to the nearest hundred. In the hundreds place is a four, and one place lower, in the tens, is a five. A five rounds up, so the four hundreds become five and everything after them becomes zero:

$$\mathrm{3,456.789}\approx \mathrm{3,500}$$

To hundredths it would be 3,456.79, because the 8 is followed by a 9. Always round straight from the original number, not step by step through each place value, or you may get a different result. The article on rounding explains why.