we can convert between fractions decimals and percentages because they all mean the same thing they all represent a part of a whole I'm gonna quickly go over how we do each of the conversions now I'll go over them each individually in more detail after so say we started with a decimal and we started with 0.3 if I want to change a decimal to a percentage I multiply by 100 so I can change a decimal to a percentage by x and by a hundred 0.3 times 100 it's that's the same as x in by 10 twice so times 10 once for 3 times 10 twice will be 30 and we write that as 30 with a % 30% if I wanted to change a percentage back to a decimal I'll do the opposite which is dividing by a hundred so decimal to percent times 100% back to decimal divided by a hundred to change a percentage to a fraction I can just rewrite the percentage as a fraction so a percentage is really a fraction out of a hundred Sofer the percent means 30 over a hundred so if ever you've got a percent that's the same as a fraction out of a hundred and I can simplify this fraction I can say they're both in the top and bottom are both in the ten times table so I've got three temps so to convert a percentage to a fraction we can rewrite over 100 and simplify to change a fraction back to a percentage we can either do the opposite which is make the fraction out of a hundred and then rewrite it as a percentage all we can times by a hundred so Eva times by a hundred or right over 100 to change a fraction to a decimal we take the top number and divide by the bottom number so 3 divided by 10 in this case so top / bottom or you could say numerator divided by denominator say 3 divided by 10 is 0.3 so I'm gonna go over each of these in a bit more detail now so these first questions are converting decimals to percentages to convert a decimal to a percentage we're multiplying by a hundred so we're going to multiply each of these by a hundred so zero point two four times 100 times 10 once is two point four times ten twice is 24 so it's 24 percent zero point six five times one hundred sixty-five percent 0.02 times 100 so times 10 once will be zero point two times 10 twice will be tooth 0.9 so times 10 once for nine times ten twice is 90 and 0.055 times ten once is 0.55 times ten twice and that'd be five point five so it's five point five percent five for you to try here give them again question one we've got zero point eight eight so that is 88% zero point zero one is 1% zero point three is 30% zero point nine seven is 97% and zero point five two six is fifty two point six percent so each time we're multiplying by 100 to convert from a percentage to a decimal we're gonna do the opposite so we are going to divide by a hundred so 72 percent divided by a hundred divided by 10 once we seven point two divided by 10 twice 0.70 21 percent so 21 divided by a hundred is zero point two 180 divided by a hundred divided by 10 once is eight divided by 10 twice is zero point eight six divided by a hundred so zero point six and then zero point zero 6 and 3 point 5 divided by a hundred so divided by 10 twice we've got zero point three five and then zero point zero three five so five for you to try convert the percentages to decimals so each time divided by 100 question 1 you should have zero point three for question 2 0 point 1 2 4 2 % 0.02 60% is 0.6 and 0.7% is zero point zero zero 7/10 once for 0.0 7/10 twice for 0.007 convert these percentages to fractions so remember percent means out of a hundred so percent out of a hundred so we can rewrite a percentage as a fraction out of a hundred and we're gonna simplify ounces if we can so seven percent means seven hundred seven out of 107 and 107 is a prime number 7 and a hundred aren't in the same kind of table so that is as simple as it gets 20 percent means 20 over a hundred twenty and a hundred both in that were the biggest x table is a 20 x table so it's 120 and five 20s 35 percent say 35 over a hundred and they are both in the five times table so we've got seven fives makes 35 and twenty fives make a hundred and twelve percent say 12 over 100 and we can say they're both in the four times table so we've got three twenty fifths you could have half dit and half dit again you should get the same answer okay for for you to try so give them a go question one we've got 2% so that's the same as 2 over 100 they're both even so we can half them so one fiftieth 15% is 15 over 100 and they are both in the 5 times table so it's 3 twentieths 98% is 98 over a hundred and they're both even so we can have them both 49 over 50 and 28 percent is 28 over 100 and we can do it in steps if you want we can have them both so 14 over 50 and then half again 7 over 25 you could have divided it by 4 to start with but either way you get the same answer convert these fractions to percentages so we can convert fractions to percentages by doing the opposite which is making the fraction out of a hundred so how can we make 3 temps out of 100 if we times top and bottom by the same thing the fraction stays equivalent so we can change a fraction by x and top and bottom by the same thing so to make the bottom the denominator a hundred we'd times by 10 so all times the numerator the top number by 10 as well that makes xxx 430 out of 100 is 30% 1120s for question 2 to make our bottom number our denominator 100 we're gonna multiply by 5 and whatever we multiply the bottom by we need to multiply the top by the same thing so that gives us 55 out for a hundred which is 55% and the third one to make our denominator 100 we're gonna multiply by 4 so we're gonna multiply top and bottom by four six fours are 24 24 over 100 is 24 percent ok free for you to try so give them a go question 1 let's multiply top and bottom by 2 so we've got 38 out of 100 which is 38 percent question 2 multiply top and bottom by 20 so we've got 60 out 400 or 60 percent and question 3 multiply top and bottom by 5 so we've got 15 out of 100 or 15% and the last one we're gonna convert fractions to decimals so to convert a fraction to a decimal we're gonna divide the top number by the bottom number we can always rewrite a fraction as a division so if you look at the divide sign it looks like a fraction and it's 7/10 7 temps is the same as 7/10 so if we do 7/10 we get zero point seven and that is a decimal question two we've got 13/20 and that looks complicated but what we can do is we can make it out of a hundred or make it out of ten to make our division easier so if we even multiply top and bottom by 5 to make it out of a hundred which we'll do so 13 times 5 is 65 20 times 5 is a hundred so it's 65 over a hundred and sixty-five divided by a hundred is 0.65 we could have also 1/2 top and bottom and had 6.5 over 10 and 6 point 5 divided by 10 is also 0.65 and the third one 1/6 now this one is a lot harder so we need to do 1 divided by 6 there's no way of making this an easy calculation so we are gonna have to use our short division method so how many sixes go into one so that's one point zero zero zero zero so how many sixes are going to go into one it's gonna be a decimal so I've added all these zeros I'm gonna write the six times table down the side 6 12 18 24 30 that's 5 6 is 36 is 6 squared + 42 48 54 + 60 so all the way up to 10 so how many sixes go into one that's zero and we've got one to carry over one left over how many six is going to 10 that's one with 4 left over how many six is going to forty six six six is at 36 and we've got four left over how many six is going to 40 at six with four left over how many six is going to full-teeth at six with four left over and so on so 1/6 as a decimal is 0.16 six-six-six going on forever so we can write that as 0.16 recurring if we had a calculator this would have been a lot easier we would have just written 1/6 or even 1/6 into the calculator and it would have given us the answer so we wrote 1/6 into the calculator and press the STD button it would tell us it's 0.16 recurring zero point 1 6 6 6 6 6 6 6 going on forever the calculators put a 7 on the end because the calculator was rounded we can do any fraction decimal and percentage conversion in the calculator if you start with a percentage so 26 percent use the percent button on the calculator press equals it's gonna change it to a fraction straight away for you and if you press the s2d button you're gonna get a decimal as well and if you started with a decimal the calculate will turn it into the fraction for you okay three of these for you to try so 21 over 50 doesn't look easy there we double the top and the bottom so it's 42 out 400 that's a lot easier to divide so 42 divided by a hundred is 0.44 three-fifths again 3/5 isn't very easy but we can change the calculation double top and bottom and we'll have 6 divided by 10 which is 0.6 and 2/3 if you already know what 2/3 is as a decimal you can just write down the answer it's one that people might remember all the alternative is to see how many threes going for two how many three is going to two point we'll add some zeros two point zero zero zero zero write down the three times table how many threes going to - that's zero - leftover how many threes him - 20 that's six six make 18 with two leftover how many threes going to 26 with two leftover how many threes going to 20 that six with two leftover and so on so two-thirds is 0.6 recurring 0.6 going on forever zero point six six six six six six six so that was converting between fractions decimals and percentages to finish up we've got a table here converting between fractions decimals and percentages and see if you can fill in the gaps the first one is 1/4 so we've got 1/4 which is a fraction and we need to write that as a decimal and the percentage this might be one the ones that you know and that is 0.25 as a decimal and 25% you could have done 1/4 to figure it out if you didn't know it for the second one we've got 0.2 which is a decimal to convert it to a percentage we can't imes by 100 so times by 10 twice which is 20% then to write that as a fraction that's 20 over 100 but they're both in the 20 times table so it simplifies to 1/5 36 percent as a fraction is 36 over 100 and they're both in the 4 times table so that simplifies to 9 25th and as a decimal 36 divided by a hundred is 0.36 0.18 as a percentage times by a hundred so 18 percent and then we'll write that as a fraction is 18 over 100 or we can 1/2 top and bottom 9 50th 1/3 hopefully that's one you know it's zero point 3 3 3 3 going on forever 0.3 recurring as a percentage so 0.3 going on forever times 100 is a 33.3 going on forever percent and we've got 4 percent so as a fraction 4 100 divide top and bottom by 4 is 125th or was a decimal 4 divided by a hundred is 0.04 you