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Rounding

What you'll learn

  • How to round whole numbers to the nearest hundred or thousand.
  • How to round decimals to 1, 2, or 3 decimal places.
  • How to round numbers to significant figures.
  • How to avoid common rounding mistakes in one-mark questions.

The big idea of rounding

Rounding means changing a number to a nearby, simpler number. The answer is not always exact, but it is easier to read and use.

For example, 376 rounded to the nearest hundred is 400.

A number line shows that 376 is closer to 400 than to 300.

Definition

Rounding

Rounding means replacing a number with a nearby number that is easier to work with, using the place value asked for in the question.

Key Idea

The rounding rule

Look at the digit just to the right of the place you are rounding to. If it is 0, 1, 2, 3, or 4, round down. If it is 5, 6, 7, 8, or 9, round up.

Place value: knowing which digit matters

Before rounding, you need to know the value of each digit.

In 7518:

A place value chart makes clear which digit is thousands, hundreds, tens, or units.

  • 7 is the thousands digit.
  • 5 is the hundreds digit.
  • 1 is the tens digit.
  • 8 is the units digit.
Definition

Place value

Place value means the value of a digit depending on where it is in the number, such as units, tens, hundreds, thousands, tenths, or hundredths.

Example

Rounding a whole number to the nearest hundred

Round 7642 to the nearest hundred.

The hundreds digit is kept and the tens digit decides whether to round up or down.

  1. Find the hundreds digit. In 7642, the hundreds digit is 6.

  2. Look at the digit just to the right. This is the tens digit, which is 4.

  3. Since 4 means round down, keep the hundreds digit the same.

  4. Change the digits after the hundreds place to zeros.

  5. So 7642 rounded to the nearest hundred is 7600.

Common Mistake

Changing the wrong digit

If the question says “nearest hundred”, you look at the tens digit to decide. Do not look at the units digit.

Rounding to the nearest hundred

To round to the nearest hundred:

  1. Find the hundreds digit.
  2. Look at the tens digit.
  3. Round the hundreds digit up or keep it the same.
  4. Replace the tens and units digits with zeros.
Example

Nearest hundred

Round 2491 to the nearest hundred.

Because the tens digit is 9, the hundreds digit rounds up from 4 to 5.

  1. The hundreds digit is 4.

  2. The digit to the right is the tens digit, which is 9.

  3. Since 9 means round up, the 4 becomes 5.

  4. Replace the tens and units digits with zeros.

  5. So 2491 rounded to the nearest hundred is 2500.

Tip

Quick check

A number rounded to the nearest hundred should end in two zeros.

Rounding to the nearest thousand

To round to the nearest thousand:

  1. Find the thousands digit.
  2. Look at the hundreds digit.
  3. Round the thousands digit up or keep it the same.
  4. Replace the hundreds, tens, and units digits with zeros.
Example

Nearest thousand

Round 4863 to the nearest thousand.

A number line shows 4863 is above halfway between 4000 and 5000, so it rounds to 5000.

  1. The thousands digit is 4.

  2. The digit to the right is the hundreds digit, which is 8.

  3. Since 8 means round up, the 4 becomes 5.

  4. Replace the remaining digits with zeros.

  5. So 4863 rounded to the nearest thousand is 5000.

Example

When rounding up changes the first digit

Round 9732 to the nearest thousand.

  1. The thousands digit is 9.

  2. The hundreds digit is 7.

  3. Since 7 means round up, 9 thousands becomes 10 thousands.

  4. 10 thousands is written as 10000.

  5. So 9732 rounded to the nearest thousand is 10000.

Decimal places

Decimal numbers have digits after the decimal point.

For example, in 6.47:

  • 4 is the tenths digit.
  • 7 is the hundredths digit.
Definition

Decimal place

A decimal place is a position after the decimal point. The first decimal place is tenths, the second is hundredths, and the third is thousandths.

Rounding to 1 decimal place

To round to 1 decimal place, keep one digit after the decimal point. Then look at the next digit.

Example

Correct to 1 decimal place

Write 8.36 correct to 1 decimal place.

For 1 decimal place, keep the tenths digit and use the hundredths digit to decide.

  1. One decimal place means keep one digit after the decimal point.

  2. In 8.36, the first digit after the decimal point is 3.

  3. Look at the next digit, which is 6.

  4. Since 6 means round up, the 3 becomes 4.

  5. So 8.36 correct to 1 decimal place is 8.4.

Common Mistake

Deleting instead of rounding

For 8.36 to 1 decimal place, the answer is not 8.3. You must check the next digit first.

Rounding to 2 or 3 decimal places

The same rule works for more decimal places.

  • 2 decimal places means keep two digits after the decimal point.
  • 3 decimal places means keep three digits after the decimal point.
Example

Correct to 3 decimal places

Write 4.72851 correct to 3 decimal places.

For 3 decimal places, keep 728 and use the next digit, 5, to round the thousandths digit up.

  1. Three decimal places means keep three digits after the decimal point.

  2. In 4.72851, the first three decimal digits are 728.

  3. Look at the next digit, which is 5.

  4. Since 5 means round up, the 8 becomes 9.

  5. So 4.72851 correct to 3 decimal places is 4.729.

Tip

Count carefully

When rounding to decimal places, start counting after the decimal point, not before it.

Significant figures

Significant figures are different from decimal places. They count the important digits in a number, starting from the first non-zero digit.

Definition

Significant figure

A significant figure is an important digit in a number. You start counting from the first digit that is not zero.

For example:

  • In 37.62, the first significant figure is 3.
  • In 0.4726, the first significant figure is 4.
  • In 90437, the first significant figure is 9.

Rounding to 1 significant figure

To round to 1 significant figure, keep the first important digit, then look at the next digit.

Example

Correct to 1 significant figure

Write 64.82 correct to 1 significant figure.

  1. The first significant figure is 6.

  2. Look at the next digit, which is 4.

  3. Since 4 means round down, keep the 6 the same.

  4. Replace the remaining digits with zeros if they are before the decimal point.

  5. So 64.82 correct to 1 significant figure is 60.

Example

Significant figures with a decimal less than 1

Write 0.5837 correct to 2 significant figures.

Leading zeros are skipped when counting significant figures, so 5 and 8 are the first two significant figures.

  1. Ignore the zeros at the start because they are not significant.

  2. The first two significant figures are 5 and 8.

  3. Look at the next digit, which is 3.

  4. Since 3 means round down, keep the 8 the same.

  5. So 0.5837 correct to 2 significant figures is 0.58.

Common Mistake

Counting zeros before the first non-zero digit

In 0.4726, the 0 before the decimal point is not the first significant figure. The first significant figure is 4.

Rounding larger numbers to significant figures

For big whole numbers, rounding to significant figures often means replacing later digits with zeros.

Example

Large number to 2 significant figures

Write 68542 correct to 2 significant figures.

  1. The first two significant figures are 6 and 8.

  2. Look at the next digit, which is 5.

  3. Since 5 means round up, the 8 becomes 9.

  4. Replace the remaining digits with zeros.

  5. So 68542 correct to 2 significant figures is 69000.

Common Mistake

Do not remove needed zeros

For large whole numbers, zeros at the end may be needed to show the size of the number. For example, 69000 is not the same as 69.

Deciding what the question is asking

Look for the key phrase:

  • “Nearest hundred” means use hundreds, then look at tens.
  • “Nearest thousand” means use thousands, then look at hundreds.
  • “Correct to 1 decimal place” means keep one digit after the decimal point.
  • “Correct to 2 significant figures” means keep the first two important digits.
Example

Spotting the method

Write 82.319 correct to 2 decimal places.

  1. The phrase “2 decimal places” means keep two digits after the decimal point.

  2. The first two decimal digits are 3 and 1.

  3. Look at the next digit, which is 9.

  4. Since 9 means round up, the 1 becomes 2.

  5. So 82.319 correct to 2 decimal places is 82.32.

Exam technique

In the exam

  1. Underline the rounding instruction, such as “nearest hundred” or “2 significant figures”.

  2. Circle the digit you are keeping, then check the digit immediately to its right.

  3. Make sure your answer has the right form: nearest hundred ends in two zeros, and decimal places have the correct number of digits after the decimal point.

Self review

Check yourself

  • How do you decide whether to round up or round down?

  • What is the difference between 2 decimal places and 2 significant figures?

  • When rounding 7486 to the nearest thousand, which digit do you look at?

Recap questions

1 of 5

Round 7642 to the nearest hundred.

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Rounding Revision Guide

  1. GCSE
  2. /Maths
  3. /Rounding