Rounding and Estimating

Rounding Up

Giving the complete number for something is sometimes unnecessary. For instance, the attendance at a rugby match might be 13145. But for most people who want to know the attendance figure, an answer of 'nearly 13000', or 'roughly 13100', is fine.

We can round off large numbers like these to the nearest thousand, nearest hundred, nearest ten, nearest whole number, or any other specified number.

Example

Round 13145 to the nearest thousand.

First, look at the digit in the thousands place. It is 3. This means the number lies between 13000 and 14000. Look at the digit to the right of the 3. It is 1. That means 13145 is closer to 13000 than 14000.

Remember

The rule is, if the next digit is: 5 or more, we 'round up'.4 or less, it stays at it is.

13145 to the nearest thousand = 13000.

13145 to the nearest hundred = 13100.

Decimal Places

Sometimes, rather than rounding off to the nearest whole number, you might need to be a little more accurate. You might need to include some of the digits after the decimal point.

In these cases, we can round off the number up to a certain number of decimal places.

e.g. 3.487908012 = 3.49 to 2 decimal places (2 dp)

Significant Figures

Sometimes we do not always need to give detailed answers to problems - we just want a rough idea. When we are faced with a long number, we could round it off to the nearest thousand, or nearest million. And when we get a long decimal answer on a calculator, we could round it off to a certain number of decimal places.

Another method of giving an approximated answer is to round off using significant figures.

The word significant means important. The closer a digit is to the beginning of a number, the more important - or significant - it is.

With the number 518259, the 5 is the most significant digit, because it tells us that the number is 5 hundred thousand and something. It follows that the 1 is the next most significant, and so on.

We round off a number using a certain number of significant figures. The most common are 1, 2 or 3 significant figures.