Teaching mathematics
Teaching mathematics

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Teaching mathematics

4.1 The decimal point and calculations with decimals

The decimal point is a symbol which is placed between the whole part of the number and the fraction part of the number. It signifies that the digit to its left is a units digit and the digit to its right is a tenths digit. All the rest of the digits fall into place to the left and right. Nothing more, nothing less. The decimal point is not some sort of bridge to jump over or obstacle to be overcome but many learners treat is as if it is.

Here is an example of a common mistake.

1.5 plus 1.5 equals 2.10

Since 5 + 5 makes 10, the learner has written 10 in the tenths column, presumably because they do not think that carrying over the decimal point is allowed. They see the decimal point as splitting the numbers into two parts which need to be dealt with separately.

However, a knowledge of place value means that the 1.5 is seen as 1 unit + 5 tenths, which when doubled is 2 units + 10 tenths (convert to 1 unit) which is 3 units.

1.5 plus 1.5 equals 3.0

One way of helping learners to appreciate this is to practise decimal times tables. Here are the first ten multiples of 0.3:

0.3, 0.6, 0.9, 1.2, 1.5, 1.8, 2.1, 2.4, 2.7, 3.0

It is tempting to say 0.12 after 0.9 but think about what it means in terms of the value of each digit. Bridging over the whole numbers is always the crunch point for the decimal times tables. They provide a useful exercise for helping learners see that numbers are carried into the next column on the left in just the same way as in whole numbers. They also look the same (as in having the same digits) as their related multiplication tables but including the decimal point.

You can think of all numbers as being decimals if you think of whole numbers as having an invisible decimal point after the units digit. You usually only make the decimal point visible if there are digits after it.

Activity 10 Using decimal times tables

Timing: Allow 3 minutes

Write out the first ten members of the 1.5 times table. You will know that you have them correct if the last one is 15.0.

TM_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, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 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 prospectus371