Mathematics

How Decimals indicate Fractions

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"How Decimals indicate Fractions"
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Fractions and decimals are both linked. Decimals can indicate fractions, and so fractions have a decimal equivalent.

Let us first begin, by considering how fractions can be divided. Fractions include a lower number over a higher number, like for example 1/3 or 2/8 or 5/6. These can be divided, like 1 divide by 3 to give a percentage. For example, one divided by 3 is 0.33 recurring or 33% when multiplied by 100.

As such, in this respect fractions can be converted to percentages. Some may have noted that dividing 1 by 3 gave 0.33. In fact, you can divide any fraction and it will give you some decimal number lower than one. Therefore, in this respect, decimal numbers less than 1 have fractional alternatives.

Let us say, for example 0.5. This decimal is actually the fraction of one halve. If you take the decimal, and then multiply by 100 then 0.5 is 50 and as a percentage, that is 50%. A few further examples:

0.25 x 100 = 25%

0.33 x 100 = 33%

0.75 x 100 = 75%

In fact, some may note that the percentages are really the same as the decimal numbers expect without the decimal in front. They are now whole numbers, and a percentage.

Therefore, as has been noted, fractions can also be divided to give decimal numbers. So, any of these decimal numbers and percentages will indicate a fraction. Let us consider some examples. Twenty-five percent is one quarter, so that is the fraction of 1/4. Thirty-three percent is a third, so that is the fraction 1/3. Then, 75% is actually three quarters so that is given as 3/4.

So overall, such decimals all have equivalent fractions. A decimal like the one 0.88 can be put as 88/100 like any such decimal can be put as a fraction of 100. However, such fractions can be lowered. Consider the example here, and both 88 and 100 can be halved as 44/50. Then, this fraction can be lowered further to 22/25. You will find that 22/25 is still the same as 88/100.

It should be noted that a decimal such as .351 should really be rounded down to two decimal places. So, in this example it will be .35, more like 35%, which is 35/100 or alternatively 7/20.

So as percentages, decimals indicate fractions. They can be converted to fractions, by rounding down and taking the decimal as whole number which will be under 100.

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