Rounding

Rounding means writing a number as a simpler number that is close to it. For example, a journey of 38 miles is about 40 miles, to the nearest 10.

To round to the nearest 10, find the multiples of 10 just below and just above your number, and choose the one that is nearer. Rounding to the nearest 100 or the nearest 1000 works in the same way.

If a number is exactly halfway, round it up. So 65 is 70 to the nearest 10, and 250 is 300 to the nearest 100.

In the exam you are asked to write a number correct to the nearest 10, 100 or 1000, to the nearest whole number, to a number of decimal places, or to a number of significant figures, usually for 1 mark. On a calculator paper a common question asks you to work something out, write down all the figures on your calculator display, and then round your answer. Many longer questions also end by asking for an answer correct to 1 decimal place or 3 significant figures.

You don't need a number line every time. Find the digit in the place you are rounding to. Then look at the digit straight after it, the deciding digit.

• If the deciding digit is 0, 1, 2, 3 or 4, the digit you are keeping stays the same.
• If the deciding digit is 5, 6, 7, 8 or 9, the digit you are keeping goes up by 1.

In a whole number, fill every place after the one you keep with a zero. The zeros keep each digit in its place, so the rounded number stays about the same size as the original.

For 367 to the nearest 10, the tens digit is 6 and the deciding digit is 7. So 6 tens go up to 7 tens, and the units digit becomes a zero, giving 370 again.

Decimal places are the places after the decimal point: tenths, then hundredths, then thousandths. Rounding to 2 decimal places means keeping two digits after the point.

The deciding digit is the one straight after the last place you keep, and the rule is the same as before. Then remove every digit after the last place you keep. Don't write zeros in their place.

If the digit you keep is a 9 and it has to go up, it becomes 10. Write 0 and carry 1 to the place on its left, as you do when adding. So 2.697 is 2.70 to 2 decimal places. Keep the final zero: it shows the answer has 2 decimal places.

Two phrases are worth knowing. To the nearest whole number means no decimal places, so the deciding digit is the tenths digit: 12.61 is 13 to the nearest whole number. For money in pounds, to the nearest penny means 2 decimal places, because a penny is one hundredth of a pound.

Significant figures are counted from the first digit that is not zero. That digit is the 1st significant figure, the digit after it is the 2nd, and so on. Zeros after the 1st significant figure still count.

Zeros at the start of a decimal are not significant figures. They only hold the other digits in their places.

Round in the same way: keep the significant figures you need and look at the next digit. If the digits you drop come before the decimal point, fill their places with zeros. In a small decimal, keep the zeros at the start.

Read which one the question asks for. 15.382 is 15.38 to 2 decimal places, but 15 to 2 significant figures.

In a calculation, keep all the figures until the very last step. Then round the final answer once. Rounding part of the way through can make the final answer wrong.

For example, 2 \times 4.36 = 8.72, which is 8.7 to 1 decimal place. If you round 4.36 to 4.4 first, you get 2 \times 4.4 = 8.8, which is wrong.

Always round the original number, not one you have already rounded. 3.648 is 3.6 to 1 decimal place. Rounding it to 3.65 first and then to 1 decimal place would give 3.7, which is wrong.

Many different numbers round to the same answer. Suppose a whole number is 80 to the nearest 10. The smallest it could be is 75, because 75 is halfway and rounds up to 80. The largest it could be is 84, because 85 would round up to 90.

Decimals work in the same way. Suppose a number has 2 decimal places and is 6.2 to 1 decimal place. It could be anything from 6.15 up to 6.24

• Rounding to the wrong place. Find the digit in the place the question asks for before you look at anything else.
• Leaving the digit as it is when it should go up. Always look at the next digit: 5 or more means the digit you keep goes up by 1.
• Losing the zeros in a whole number. Fill the places up to the decimal point with zeros, so 4180 to 2 significant figures is 4200, not 42
• Mixing up decimal places and significant figures. Decimal places count from the decimal point; significant figures count from the first digit that is not zero.
• Counting the zeros at the start of a decimal. Start counting at the first digit that is not zero, and keep the zeros in your answer.
• Rounding too early. Write down all the figures on your calculator display, keep them until the end of a calculation, then round once.