We can write any fraction as a decimal.

We do this by treating it as a division, which we can do either using pen and paper or with our calculator.

Some decimals are terminating, i.e. to the right of the decimal point will be a limited number of digits.

Some decimals (e.g. 1/3) are non-terminating, i.e. to the right of the decimal point the digits go on forever (although your calculator can’t show them all).

Exercise

Let’s try exercise 10F on page 152 of the textbook without using our calculators (or only use them to check after doing the question.

The answers are below:

Extension exercise

If we want to change a recurring decimal into a fraction, there is a very nice technique to do it. Let’s try out this technique for:

• 0.88888…
• 0.141414…..

Let’s use this technique on question 2 and question 6 of exercise 10G on page 153 of our textbook.

The answers are below: