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Video: Converting Fractions to Decimals

Tim Burnham

Convert 16/20 to a decimal.

03:44

Video Transcript

Convert sixteen twentieths to a decimal. Well we’re gonna look at two different ways of attacking this question. The first way is gonna be to find an equivalent fraction with ten or a hundred or a thousand and so on as a denominator. And the second way is just to do the numerator divided by the denominator in a calculation.

So let’s look at the first method first then. So we’re trying to find a denominator of ten or a hundred or a thousand and so on. Well sixteen and twenty, if I divide both of those by two, I get a denominator of ten. Well sixteen divided by two is eight and twenty divided by two is ten. Now if we think about decimals, the first decimal place is the number of tenths. The second decimal place is the number of hundredths. The third decimal place is the number of thousandths and so on. Now we’ve got eight-tenths. So that means we’ve got an eight in the tenths column. Now we haven’t got any whole numbers. So we’ve got a zero over here and we haven’t got any hundredths or any thousandths. So the answer is simply nought point eight.

Now just before we move on, we could have said twenty times five is a hundred. So I could’ve multiplied my numerator and my denominator by five, which would’ve given me eighty hundredths. Now if we’d taken that approach, we’d have been left in a slightly awkward situation, because we’d be trying to put eighty in our hundredths column. Well because it’s just a column, it can only have one digit in it. So to write eighty in the hundredths column, we have to write the zero and we carry the eight over to the next biggest column. And we’d write that as zero carry eight. And we’ve got no whole numbers, so we’d have zero in this position as well.

Now in both cases, there aren’t any digits beyond the eight. So all of these would be zeros. These trailing zeros, we don’t normally bother writing out. So in both cases, we have ended up with the same answer of nought point eight. And we could write that as we say as nought point eight zero on or nought point eight zero zero and so on. But we wouldn’t normally bother. We’d just write nought point eight.

So let’s look at the other method then: the numerator divided by the denominator. Well that would be sixteen divided by twenty. That looks like quite a tricky calculation to do. But if we look carefully at the fraction, we can know that it cancels first, four is going to sixteen and four is going into twenty. So sixteen twentieths actually can be simplified. Sixteen divided by four is four and twenty divided by four is five. So rather than calculating sixteen divided by twenty, we could calculate four divided by five.

So let’s write this calculation out then. Four, I’m gonna write four point zero zero, divided by five. Now let’s just copy up our decimal point here. And how many times do five go into four? Well they don’t. Five is bigger than four, so that goes zero times. So now we need to consider how many times do five go into forty, so ignoring that decimal point for now. Well five goes into forty eight times. And eight times five is forty. Now the difference between forty and forty is zero. So we’ve got our correct answer now, nought point eight. So just thinking about those two methods, if your denominator will easily convert a ten or a hundred or a thousand and so on, then I would suggest method one is probably the easiest. If it doesn’t though, then you’re gonna have to get into doing some long or short division.