This is ok as a percentage does not have to be less than 100.ī) Multiplying 0.29 by 100 gives the answer as 29%.Ĭ) 0.725 multiplied by 100 is equal to 72.5%. ExampleĬonvert the following decimals to percentagesĪ) Multiplying 1.83 by 100 gives the answer of 183%. Therefore, a decimal of 0.45 converts to a fraction by multiplying by 100, so we get 0.45 100 = 45%. Instead of dividing the number by 100 we must simply multiply by 100.
If we were to solve a problem where we had to convert from a decimal to a percentage we can simply reverse the process that was outlined earlier for converting from a percentage to a decimal. Converting from a decimal to a percentage This can be done by multiplying both the top and bottom of the fraction by 5: now we can simply see that is equal to 85% since % means ‘out of 100’. To do this we must find a fraction that is equivalent to with a denominator of 100. This is done by the rules that we explored in the last module on equivalent fractions. This is because a percentage must be ‘out of 100’, therefore we must convert the fraction to have a denominator of 100 before we can change it to a percentage. If we wish to convert from a fraction to a percentage, we must do a little bit more work than if we were to convert the other way around. Converting from fractions to a percentage This is the same method used for any other percentage that we want to change to a decimal. So if we were to change 89% to a decimal we simply must calculate. It is fairly straightforward to convert a percentage to a decimal also we simply have to divide the percentage by 100. This then shows that we can very easily convert a percentage into a fraction by simply writing the number over 100. So if we wanted to denote 50 per cent we would write 50%, which is the same as 50 out of 100. The word ‘per cent’ really just means ‘out of 100’ so we know that a percentage is always related to 100. We are simply using it as a piece of notation that has the equivalent meaning to /100.Percentages are used in much the same way as decimals and fractions in that they show a link between two values. So what about multiplying the denominator? That's taken care of by the % sign outside the bracket (remember that % is the same as /100).Īt no point are we multiplying by %. There's a x 100/1 inside the brackets, which multiplies the numerator by 100. This is seen in the red box with the quote from the textbook. Sticking on a % sign is the same as multiplying the bottom by 100. You may have noticed that I said "we need to multiply top and bottom by 100", and then I just did a single multiplication of 100 (ie multiplying the top). Sticking a % sign on the end is the same as saying "out of 100". Shorthand, you could do (50/200)*100 = 25 And then we would write the answer as "25 out of 100" or 25%. Another way of writing 25/100 is 25% (note we are not involving the % symbol in the multiplication itself). We achieve this by multiplying both top and bottom by 100. Now, remembering that percentages have 100 as the denominator, we need to get 100 on the bottom instead of 1. This could just as well be written 0.25/1. You could think of this as a fraction with 1 as the denominator.Į.g. 50/200) into a calculator, the calculator returns a decimal value. When you type a division expression (e.g.
If you're using a calculator, that's where many people get confused about what multiplication to do. If you're doing this by hand with "nice" numbers, it's just a case of fraction manipulation.
Then, you have an expression that can be read as "x out of 100" and, hey presto, there's your percentage. Turning a fraction into a percentage is really just a case of finding the equivalent fraction which has 100 as the denominator (ie x/ 100).
You can think of % as being equivalent to writing /100. It means "out of one hundred" (literally, "per cent"). The % sign is simply a symbol with a meaning. You have then had to multiply that number by 100 in your head to get the answer I have highlighted in green.ġ00% is not really a number as such, therefore you cannot exactly "multiply by 100%".ġ00% means "100 out of 100", or 100/100. The person in red has it right when they say: the calculation you have done gives you the answer I have highlighted in yellow.
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