Everyday maths 1
Everyday maths 1

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Everyday maths 1

4 Decimals

Described image
Figure 15 Looking at 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 the builder in the last activity made a wrong measurement, the whole kitchen extension could be affected.

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.

Described image
Figure 16 What is a decimal point?

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 . one divided by 10s one divided by 100s one divided by 1,000s

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

5.1 = 5 and one divided by 10

67.2 = 67 and two divided by 10

8.01 = 8 and one divided by 100

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 (nine divided by 10)

6 hundredths (six divided by 100)

3 thousandths (three divided by 1,000)

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

  1. Four children are taken to the 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?
  1. Six athletes run a race. Their times, in seconds, are as follows:
Sonia 10.95
Anjali 10.59
Anita 10.91
Aarti 10.99
Sita 10.58
Susie 10.56
  • Who gets the gold, silver and bronze medals?
  1. In a gymnastics competition, the following points were awarded to four competitors. Who came first, second and third?
Janak 23.95
Nadia 23.89
Carol 23.98
Tracey 23.88

Answer

  1. 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.
  1. 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 medals go to:
    • Susie (10.56 secs): gold
    • Sita (10.58 secs): silver
    • Anjali (10.59 secs): bronze
  1. 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 scores 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 top three competitors are:
    • Carol (23.98)
    • Janak (23.95)
    • Nadia (23.89)
FSM_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus