When you want to show a fraction as a percentage just remember that 100% is a whole amount – in decimal terms it can be shown as the number 1. When you divide one into thirds you split the whole amount (1) into three parts. So when you show 100% as thirds you split 100 into three equal parts and multiply this number by the number of thirds in your fraction.

1. The bottom number (the denominator) in all thirds fractions is 3.
2. Imagine you have an apple and you cut it into three pieces – each piece is one third of the apple.
3. One apple is 100% of the apple – so let’s cut the percentage value for a whole (100) into 3 pieces as well!
4. 100 ÷ 3 = 3.333…
5. Every top number in the fraction (the numerator) represents one third of 100%.
6. Multiply the numerator by the percentage value of each piece to show the fraction as a percent.

The fourth item in the list above contains a special value. When you see a decimal amount that has three dots at the end it means that it is a recurring value. This is more easily visualised when you look at dividing the number ten by three.

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10 ÷ 3 = 3 with 1 left over – so now divide the 1 that is left by three 1 ÷ 3 = 0.3 with 0.1 left over – so now divide the 0.1 that is left by three 0.1 ÷ 3 = 0.03 with 0.01 left over – so now divide the 0.01 that is left by three 0.01 ÷ 3 = 0.003 with 0.001 left over – so now divide the 0.001 that is left by three…

Can you see that we are in a never ending run of division, with an amount left over that decreases by a decimal place each time? You could continue this run of division for ever and you would not reach a final amount – it is an infinitely repeating pattern so it is known as a recurring value.

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You can use a method called rounding to shorten any number that has a lot of decimal places, including recurring decimals. To do this you look at the value of the number to the right of the decimal place you want to end with; if this number is less than five you leave your final number as it is, if the number is more than five then you increase your final number by one.

Here’s an example, let’s shorten 6.84610876153 to three decimal places. We start with the number that is one decimal place longer than where we want to end, 6.8461. The number at the end of this figure is a 1 – it is lower than 5 so we round down to 6.846. If the number to shorten was 6.84690876153 then the number that is one decimal place longer than where we want to end, 6.8469. The number at the end of this figure is a 9 – it is higher than 5 so we round down up 6.847.

With the above in mind, here are each of the thirds fractions shown as a percentage and the workings behind the answer.

1/3 as a percent

1. Divide 100 by the denominator: 100 ÷ 3 = 33.333…
2. Multiply this number by the nominator: 33.333… × 1 = 33.333…
3. Tidy the recurring figure. If you want to round to the nearest whole number then start with 33.3 – the final 3 is lower than 5 so we leave the last whole 3 as a 3.

So what is 1/3 as a percentage? The answer is 33%

2/3 as a percent

1. Divide 100 by the denominator: 100 ÷ 3 = 33.333…
2. Multiply this number by the nominator: 33.333… × 2 = 66.666…
3. Tidy the recurring figure. If you want to round to the nearest whole number then start with 66.6 – the final 6 is higher than 5 so we round it up to 7.

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What is 2/3 as a percentage? The answer is 67%.

3/3 as a percent

1. Divide 100 by the denominator: 100 ÷ 3 = 33.333…
2. Multiply this number by the nominator: 33.333… × 3 = 99.999…
3. Tidy the recurring figure. If you want to round to the nearest whole number then start with 99.9 – the final 9 is higher than 5 so we round up the last 9 to make 100.

So what is 3/3 as a percentage? The answer is 100%.

Remember this point about three thirds (3/3) – if the numerator can be divided by the denominator where the result is a whole number, you can reduce the fraction.

3 ÷ 3 = 1

So the fraction could also be expressed as 1/1 – 1 part of 1 is 1 – it is all of it, the whole amount – it is 100%!

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