Lesson video

Hi, I'm Mrs. Danny, and in today's lesson, we're going to be looking at changing fractions into recurring decimals using short division.

Here are some decimals.

You may recognise these as terminating decimals.

They have a finite number of decimal places.

They're quite easy to write as fractions as their digits are in the 10ths, 100ths or 1000ths place value columns.

For example, 0.

3 can be written as three-tenths.

4.

92 is equivalent to four and 92 hundredths.

Let's look at some recurring decimals.

Recurring decimals contain one digit or a group of digits that repeats indefinitely.

We use special notation to write recurring decimals.

As you can see here, you can use three or more dots at the end of the number to indicate a recurrence.

Well, there is a more efficient way to write recurring decimals.

We can use dots above the first and last repeating digits.

Here are some more examples for you to look at.

Here are some questions for you to try.

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

Here are the answers.

Notice that not 0.

1 recurring can be written more efficiently.

We're now going to write five-sixths as a decimal.

Remember that five-sixths can also be written as five divided by six.

We use short division to help us convert the fraction to a decimal.

Make sure you place the numerator, in this case five, and the denominator six, in the correct positions.

The denominator always goes on the left.

Now we can start from the division.

Five divided by six gives us zero with a remainder of five.

Remember to write down the decimal points, and continue to divide.

You will notice that the three is starting to appear again, and again, it's recurring.

So we can write that answer as 0.

83, with a dot above the three to show that only the three is recurring.

Here is a question for you to try.

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

Here is the answer.

You can see that we're using short division, make sure one and six are in the correct positions.

One divided by six gives us zero with a remainder of one.

10 divided by six gives us one with a remainder of four.

And you will notice that this starts to recur.

So our final answer is 0.

16, with a dot above the six to show that just the six is recurring.

Here is a question for you to try.

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

Here is the answer.

You can use short division to turn these decimals into fractions.

So you'll do one divided by nine and five divided by 11, etc.

Take care with three-sevenths though.

Make sure that you do the division enough time to see how many digits are actually recurring.

Also, when you write your answer, make sure that the dots go above four and one only.

Here is another question for you to try.

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

Here is the answer.

Two-thirds and six-ninths are both equal to 0.

6 recurring.

You may have spotted that six-ninths simplifies to two-thirds and saved yourself a little bit of time on this one, by spotting that the fractions are equivalent, and therefore the decimals must be as well.

Here is a question for you to try.

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

Here is the answer.

Firstly, you need to convert the fractions to decimals.

All of them are recurring except three-tenths, three tenths is 0.

3 and this is a terminating decimal.

You can still use short division to calculate three divided by 10.

But it may be faster to just do it in your head.

Now we consider each of the place values for each digit.

So 0.

2 recurring is the smallest, followed by two-sevenths.

But look carefully at one-third and three-tenths.

One-third is 0.

3 recurring, so there are an infinite number of threes after the decimal point, whereas three-tenths is just 0.

3.

So that's one three after the decimal point.

Therefore one-third is larger.

Here is another question for you to try.

You might need a little reminder about prime numbers for this question.

A prime number has exactly two factors, itself and one.

For example, 13 is prime because it only has two factors, one and 13.

Nine isn't prime because it has three factors, one, three and nine.

Pause the video now to complete your task and restart once you're finished.

Here is the answer.

The prime numbers are two, three, five, seven, 11, etc.

You may have noticed from previous questions that you've done and your calculations that thirds and sevenths do produce recurring decimals.

However, fractions with a denominator of two or five do not.

For example, two-fifths is 0.

4, which is a terminating decimal.

That's why this statement is only sometimes true.

Here is a question for you to try.

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

Here is the answer.

All of these fractions have a denominator of nine, and when you convert them, you can see that, if the numerator is one, we get 0.

1 recurring.

If the numerator is two, you get 0.

2 recurring.

So by the time you started to convert six-ninths and seven-ninths, you would realise that the numerator can be used as the recurring digit after the decimal point.

Here is a final question for you to have a go at.

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

He is the answer to the final question.

I really like this question.

Once you've calculated each fraction as a recurring decimal, all you have to do is spot the pattern.

You can see that the same digits recur.

But they just have different starting points for each fraction, amazing.

That's all for today's lesson.

Thank you for watching.