Rounding: Integers, decimal places, significant figures

In a nutshell

There are three different types of ways to round numbers. One way of rounding involves rounding to the nearest whole number, ten, hundred, thousand or million. Other ways of rounding include rounding to the nearest decimal place or the nearest significant figure.

Rounding to whole numbers

You can round any number to the nearest whole number, nearest ten, nearest hundred, etc. To round to the nearest whole number, look at the number after the decimal point to see whether to round up or down. To round to the nearest ten, look at the number in the units column to see whether to round up or down.

In the same way, when rounding to the nearest hundred, thousands or millions, look at the digit to the right, or the digit that is one place value lower to see whether to round up or down. If the digit is smaller than five, round down and if the digit is five or bigger, then round up.

Example 1

Round $43.6$ to the nearest whole number.

To round to the nearest whole number, look at the number after the decimal point. As $6$ is bigger than $5$ , round up.

$43.6$ rounded to the nearest whole number is $\underline{44}$ .

Example 2

Round $12 \ 346$ to the nearest hundred.

To round to the nearest hundred, look at the number in the tens column. As $4$ is less than $5$ , round down.

$12 \ 346$ rounded to the nearest hundred is $\underline{12 \ 300}$ .

Decimal places

To round to the nearest decimal place, look at the digit to the right, or the digit that is one place value lower to see whether to round up or down. If the digit is smaller than five, round down and if the digit is five or bigger, then round up.

Example 3

What is the value of $17.342$ to $2$ decimal places?

To round to $2$ decimal places, look at the digit in the $3rd$ decimal place. As $2$ is less than $5$ , round down.

$17.342$ rounded is $\underline{17.34 \ (2 \ d.p.)}$ 

Significant figures

The first significant figure in a number is the first non-zero digit starting from the left. The second significant figure is the digit to the right, then the third significant figure is to the right again, and so on. Zero can be counted as a significant figure from the second significant figure onwards.

Example 3

What is the value of $0.003708$ to $3$ significant figures?

The first significant figure starts at the digit $3$ . The second significant figure is $7$ , and the third significant figure is $0$ . To round to $3$ significant figures, look at the next digit. As $8$ is bigger than $5$ , round up.

$0.003708$ rounded is $\underline{0.00371 \ (3 \ s.f.) }$ 