# 4 Decimals

Can you think of any examples of when you might come across decimal numbers in everyday life?

If you’re dealing with money and the decimal point is not placed correctly, then the value will be completely different, for example, £5.55 could be mistaken for £55.50.

Likewise with weights and measures: if a nurse gave the wrong measure of medicine to a patient this could make them very ill or put their life at risk.

This section will help you to understand:

- the value of a digit in a decimal number
- ways of carrying out calculations with decimal numbers
- approximate answers to calculations involving decimal numbers.

You looked at place value in the section on whole numbers. Now you’ll take a look at decimals.

So what is a decimal point?

It separates a number into its whole number and its fractional part. So in the example above, 34 is the whole number, and the seven – or 0.7, as it would be written – is the fractional part.

Each digit in a number has a value that depends on its position in the number. This is its place value:

Whole number part | . | Fractional part | |||||
---|---|---|---|---|---|---|---|

Thousands | Hundreds | Tens | Units | . | Tenths | Hundredths | Thousandths |

1000s | 100s | 10s | 1s | . | s | s | s |

Look at these examples, where the number after the decimal point is also shown as a fraction:

5.1 = 5 and

67.2 = 67 and

8.01 = 8 and

## Example: Finding values

If you were looking for the place value of each digit in the number 451.963, what would the answer be?

Hundreds | Tens | Units | . | Tenths | Hundredths | Thousandths |
---|---|---|---|---|---|---|

4 | 5 | 1 | . | 9 | 6 | 3 |

So the answer is:

4 hundreds

5 tens

1 unit

9 tenths ()

6 hundredths ()

3 thousandths ()

Use the example above to help you with the following activity. Remember to check your answers once you have completed the questions.

## Activity 11: Decimal dilemmas

- Jo works as a learning support assistant in a school. She accompanies four of the children to a funfair. One of the rides, the Wacky Wheel, has the following notice on it:
- For safety reasons, children must be over 0.95 m tall to go on this ride.

- Margaret is 0.85 m tall.
- David is 0.99 m tall.
- Suha is 0.89 m tall.
- Prabha is 0.92 m tall.
- Who is allowed to go on the ride?

- Six ambulance drivers are responding to the scene of a major incident. The time it takes each person to arrive, in minutes, are as follows:

Sonia | 10.95 |

Anjali | 10.59 |

Anita | 10.91 |

Aarti | 10.99 |

Sita | 10.58 |

Susie | 10.56 |

- Who arrives at the scene first, second and third?

- Prospective nursing students are required to complete a maths assessment under timed conditions. The test times of four students are shown below. Who completed the assessment in the fastest, second fastest and third fastest time?

Janak | 23.95 |

Nadia | 23.89 |

Carol | 23.98 |

Tracey | 23.88 |

### Answer

- Any child that is more than 0.95 m tall will be allowed on the ride. So to answer the question you need to compare the height of each child with 0.95 m.

Tenths | Hundredths | |
---|---|---|

Margaret | 8 | 5 |

David | 9 | 9 |

Suha | 8 | 9 |

Prabha | 9 | 2 |

- Comparing the tenths tells us that only two children may possibly be allowed on the ride: David and Prabha.
- If we go on to compare the hundredths, we see that only David is taller than 0.95 m.
- So only David would be allowed on the Wacky Wheel.

- You need to compare the tens, units, tenths and hundredths, in that order.

Tens | Units | . | Tenths | Hundredths | |
---|---|---|---|---|---|

Sonia | 1 | 0 | . | 9 | 5 |

Anjali | 1 | 0 | . | 5 | 9 |

Anita | 1 | 0 | . | 9 | 1 |

Aarti | 1 | 0 | . | 9 | 9 |

Sita | 1 | 0 | . | 5 | 8 |

Susie | 1 | 0 | . | 5 | 6 |

- All of the times have the same number of tens and units, so it is necessary to go on to compare the tenths.
- The three times with the lowest number of tenths are 10.59, (Anjali), 10.58 (Sita) and 10.56 (Susie). If we now go on to compare the hundredths in these three times, we see that the lowest times are (lowest first): 10.56, 10.58 and 10.59.
- So the first, second and third drivers to arrive were:
- Susie (10.56 secs): first
- Sita (10.58 secs): second
- Anjali (10.59 secs): third

- Again, we need to compare the tens, units, tenths and hundredths, in that order.

Tens | Units | . | Tenths | Hundredths | |
---|---|---|---|---|---|

Janak | 2 | 3 | . | 9 | 5 |

Nadia | 2 | 3 | . | 8 | 9 |

Carol | 2 | 3 | . | 9 | 8 |

Tracey | 2 | 3 | . | 8 | 8 |

- All the times have the same number of tens and units. Looking at the tenths, two scores (23.95 and 23.98) have 9 tenths. If you compare the hundredths in these two numbers, you can see that 23.98 is bigger than 23.95.
- To find the third highest number, go back to the other two numbers, 23.89 and 23.88. Comparing the hundredths, you can see that 23.89 is the higher number. So the three fastest times are:
- Carol (23.98)
- Janak (23.95)
- Nadia (23.89)