Skip to 0 minutes and 7 seconds PAULA KELLY: So let’s have a look now, how we could change between a fraction to a decimal.

Skip to 0 minutes and 12 seconds MICHAEL ANDERSON: So when we’re working with decimals, we’re working with tenths. We’re working with hundredths. We’re working with thousandths. So what we’re going to look to do is convert our fraction into an equivalent fraction that has a ten or a hundred or a thousandth as the denominator. So let’s have a look at 2/5.

Skip to 0 minutes and 30 seconds PAULA KELLY: So let’s go back to our example. So we have our 2/5. And just to see that visually, we’ve got our 5 equal size boxes. I’m going to have two of them. OK.

Skip to 0 minutes and 44 seconds So that’s my visual representation. What’s happening here?

Skip to 0 minutes and 48 seconds MICHAEL ANDERSON: So if we look at the fifths, we know that actually, in the 5 times tables, 10 is the next number to appear. So what we’re going to do is we’re going to change this into a fraction that has 10 as the denominator. To get from 5 to 10, we have to multiply by 2. So we’re going to do the exact same with the numerator, with that 2 on top. We’re going to multiply that by 2 as well. And that’s going to give us 4/10.

Skip to 1 minute and 16 seconds PAULA KELLY: OK. And very conveniently, we have the same size box.

Skip to 1 minute and 20 seconds MICHAEL ANDERSON: Yep.

Skip to 1 minute and 20 seconds PAULA KELLY: It’s been cut now into 10 slices. I can tell quite quickly because each of my 5 pieces has been halved. So I have double the amount of slices, same as we’ve doubled our numerator.

Skip to 1 minute and 33 seconds MICHAEL ANDERSON: So if we shade them in, hopefully we’ll shade in 4 out of 10.

Skip to 1 minute and 37 seconds PAULA KELLY: OK, let’s see. So for each one, shade in two. We’ll keep the height the same, because the amount we’re having isn’t changing. OK. So out of my 10 pieces, I now have 4.

Skip to 1 minute and 50 seconds MICHAEL ANDERSON: So what we’ve done there is put it in a really good position for changing this fraction into a decimal. If we think about decimals, well, we’ve got our ones here, the decimal point, and then next we’ve got the tenths. So if we’re thinking of the fraction 4/10, well, we’ve got 0 units, 0 ones, and we’ve got 4 tenths. So as a decimal, that’s 0.4.

Skip to 2 minutes and 16 seconds PAULA KELLY: And that makes sense for my diagram, because I can see I have not a whole one. I have 0 whole ones. All of these are tenths. And I have 4 of them, so I have 4 tenths.

Skip to 2 minutes and 25 seconds MICHAEL ANDERSON: Perfect. So let’s have a look at another example of converting a fraction into a decimal.

Skip to 2 minutes and 32 seconds PAULA KELLY: OK, so we’ve got now 4/25.

Skip to 2 minutes and 37 seconds As you mentioned earlier, if you’re going from fractions to decimals, we could do the denominator of 10, 100, 1,000. Multiples of 10, basically. So 4/25. I’ve got this box here. It’s been cut into 25 equal pieces. And I’m going to shade in that I have 4 of them.

Skip to 2 minutes and 57 seconds MICHAEL ANDERSON: Now, it doesn’t really matter which 4 boxes we’ve shaded there. If we shade in any 4, that’ll be 4/25.

Skip to 3 minutes and 3 seconds PAULA KELLY: The area will be the same.

Skip to 3 minutes and 6 seconds MICHAEL ANDERSON: So if we’re thinking about 25, we’re going to try and multiply that by something to get to either a 10, or 100, or 1,000. So in our 25 times tables, 25, 50, 75, 100. So it seems to be that we’re going to have to multiply by 4.

Skip to 3 minutes and 23 seconds PAULA KELLY: OK, so let’s have 100 as our denominator. We have multiplied by 4. So we have an equivalent fraction. We do the same to top and bottom. So 4 fours give me 16. And very conveniently, we have 100 squares here. I’m going to shade in– I’ve got 16 of them. To save me some counting, I know it’s 100 square. So 10 by 10. So I’ve got a whole lot of 10. And my remaining– I’ve got 6 there.

Skip to 3 minutes and 55 seconds MICHAEL ANDERSON: And that’s the exact same area as we had here.

Skip to 3 minutes and 58 seconds PAULA KELLY: Yeah. And if you notice, each one of these has 4 smaller boxes. So I’ve got 4 lots of these. So 16 altogether.

Skip to 4 minutes and 6 seconds MICHAEL ANDERSON: Perfect. OK, so we can think of this 16/100 in tenths and in hundredths. And it’s really convenient that we’ve got it coloured in this way, because if we look at this box and this box, this is a box that’s been split up into tenths. And this one has been split up into 100 smaller squares. So if I colour in this box here, that’s the same length, it’s the same area as 10 of our 16ths. I’ve now got 6 left over. So I can colour in 6 here. One, two, three, four, five, six. And these two areas combined are the same area as the 16 hundredths here.

Skip to 4 minutes and 52 seconds PAULA KELLY: So we’re trying to show our fraction as a decimal. We’ve decided we need to have 100 as our denominator. So in our table, we’re going to have our ones. We have got some units, our ones. We have got some tenths. So I’ll label this as our tenths. We’ve also got some hundredths, so we’ll label this as our hundredths.

Skip to 5 minutes and 17 seconds MICHAEL ANDERSON: So if we look at this diagram, what I’ve actually shaded in is 1 out of the 10 pieces. So we have 1/10. So I can put the value of 1 in here. Now, 4/25 or its equivalent fraction 16/100 is less than 1. We have 0 units. So it’s going to be 0.1. But we’re not quite finished because we have to look at the hundredths. In here, we shaded in 6 of them. So we have 6 hundredths. So I can put a 6 in that column there.

Skip to 5 minutes and 45 seconds PAULA KELLY: OK. And as you mentioned, it’s going to be less than 1. We haven’t got any full boxes shaded in. If we also notice that our fraction is actually a division, so 16 divided by 100. All of our numbers are actually moved two places smaller.

Skip to 6 minutes and 1 second MICHAEL ANDERSON: To give us 0.16 as the decimal equivalent as to 4/25 is a fraction.

# Fractions as decimals

In this step we look to understand the relation between numbers expressed as fractions and expressed as decimals.

Paula and Michael concentrate upon understanding the mathematical structure, rather than just a procedural explanation of ‘how to’ convert a fraction to a decimal. If you are not familiar with decimal place value, we also cover this in the video.

The first example converts a fraction to a decimal which has one decimal place, therefore being made of up tenths.

The second example converts a fraction into a decimal containing two decimal places therefore being made up of tenths and hundredths.

The place value grid is shown below for reference:

© National STEM Learning Centre