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.

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.

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.