Lesson video

Hi, I'm Mrs. Dennett.

And in today's lesson, we're going to be looking at recurring decimals where one digit after the decimal point, is fixed.

There are different types of recurring decimal that you need to be aware of.

Some may have one repeating digit, or a group of repeating digits.

They may have some digits after the decimal point that do not repeat, such as 0.

04 recurring in the top left.

Or 77.

365 recurring in the middle bottom row, which has two fixed digits after the decimal point, and only the five repeating.

Here is a question for you to try.

Pause the video to complete the task and restart when you've finished.

Here is the answer.

What is the same? All the decimals have a two in the hundreds column, and are written to two decimal places.

All of them recur in some way, but crucially, some have one recurring digit and others have two.

Notice 0.

62 recurring and 0.

02 recurring, have a fixed digit, after the decimal point.

And it's these types of decimals we'll be concentrating on in today's lesson.

To change 0.

62 recurring into a fraction, we use algebra.

But x equal 0.

62 recurring.

One digit is repeating, so we multiply by 10, 10 x equals 6.

2 recurring.

We then subtract x from 10x, to eliminate the recurring part of the decimal.

Take care with the place value columns, and your subtraction methods.

We are left with 9x equals 5.

6.

To make life easier, we're going to make this decimal into a whole number.

So we need to multiply by 10.

Remember to do this to both sides, to keep the equation balanced.

Then divide 56 by 90 and simplify.

So 0.

62 recurring is equivalent to 28 over 45.

Here's a question for you to try.

Pause the video to complete this task, and restart when you've finished.

Here is the answer.

We multiply by 10 because there's one recurring digit.

Subtract x from 10x to get 9x equals 5.

1, multiply both sides of the equation by 10, so that we can make 5.

1 into an integer.

And then solve and simplify.

So on 0.

56 recurring is equivalent to 17 over 30.

Here's another question for you to try.

Pause the video, to complete the task, and restart when you're finished.

Here is the answer.

This question is quite straightforward, but remember to simplify 46 over 90, dividing numerator and denominator by two to get 23 over 45.

Here's some questions for you to try.

Pause the video, to complete this task, and restart when you've finished.

Here are the answers.

The questions here today, you only need to multiply by 10 because there is just one digit recurring.

For questions e and f, you needed to multiply by a hundred.

Again, be very careful with the subtraction and simplifying.

Here's a question for you to try, pause the video to complete the task, and restart when you've finished.

Here is the answer.

You really need to pay a special attention to the number of recurring digits in this question.

So for the first one, we multiplied by a hundred, for the second one, times by a thousand, and for the third one, multiply by 10,000.

This question follows on from the previous question, pause the video to complete the task and restart when you've finished.

Here is the answer.

Notice that all the decimals are less than one.

They don't simplify.

They are different to the previous questions.

We have looked at because there are no fixed digits after the decimal point in any of these decimals.

Where two digits recur, the denominator is 99.

Where three digits recur, the denominator is 999, and so on.

Again, you may want to look at the answers to the previous questions to help you with this one, pause the video, to complete this task, and restart once you've finished, As these decimals have two, three, or four repeating digits, after the decimal point and the less than one, we can just write them over the number of nines, indicated by their repeating digits.

So 0.

21 recurring has two repeating digits.

So this will be 21 over 99.

Notice the two nines and the denominator.

We are using patterns to help us to spot the answers.

Here are some final questions for you to try, pause the video to complete this task, and restart when you've finished.

Here are the answers.

Question six, 0.

4 recurring, 0.

14 recurring, and 1.

4 recurring, don't have a fixed digit after the decimal points.

So when we write them as fractions, their denominators contain only nines.

For question seven, each decimal has a fixed digit after the decimal point.

So all can be written over 90, so it's easier to add them up.

And we get two thirds as our answer.

That's all for this lesson.

Thanks for watching.