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Fractions To Decimals

I wrote extensively about the importance of (and difficulties in understanding) fractions and I said that all fractions are in the end numbers which you can digit in a calculator.

Actually, ALL fractions are in the end but decimals, including 1/1 which is simply equal to 1.0000....! Or simply 1 for our comfort zone!

And of course numbers can be 2.345... or 1. 66666..., that is repeating-decimal numbers. with repeating

Now, to convert a fraction to decimals you simply have to divide the top number by the bottom number and then round-off to the degree of accuracy that you need (i.d. one, two or more positions after the point).


two thirds is equal to decimal...

2/3 = 2 : 3

= 0.6666... (the 6 goes on forever)

= 0.67 (rounding off to two decimal positions)



What is 4/7 in decimal terms? (you can use this online calculator in this case...)






Did you get it?

So divide the fraction as it were a division. That's it!


But what if you don't have a pocket calculator is there another simple way to convert fractions to decimals?

Yes there is, but only for fractions which have 10 or a power of 10 as denominator. So:

Fractions to decimals rules

1. Look if the denominator is 10 or one of its powers (100, 1'000, 10'000, 100'000 etc,,,)

2. If not, correct the fraction by converting the denominator to 10 or one of its power
(e.g. 3/5 = 6/10; 7/4= 175/100 I did it? Well I multiplied BOTH top and bottom by the same amount, so 3/5 * 2/2= 6/10 and 7/4 * 25/25 = 175/100. This is the "1" trick, in this case 2/2 and 25/25)

3. Simply read and "see" the value position of decimals
e.g 6/10 = 0.6; 175/100=0,175

4. if you cannot convert the fraction to a 10-power denominator then simply divide the two numbers like shown at the beginning of this page!


Fractions to decimals examples:

1. What decimal number is 5/100?
The solution is 5/100 = 0.05

2.What decimal number is 345/100?
The solution is 345/100 = 3.45
Because 345/100 = 300/100 + 40/100 + 5/100 = 3 + 4/10 + 5/100=
=3 + 0.4 + 0.05

3. What decimal number is 5/25?
The solution is 5/25 = 0.2
Because 5/25 = 20/100
(I multiplied BOTH denominator and numerator by 4; this is the "1" trick:
you are allowed to multiply anything by 1 because this operation leave everything unchanged.
In this case the "1" is 4/4)
so 5/25 = 20/100 = 2/10
(I now simplified both denominator and numerator by dividing BOTH of them by 10
(again, this is the "1" trick, here the 1 is 10/10).
And finally, 2/10 = 0.2

palm of hand: wait! I can explain to you further!WAIT!

Not clear enough?

Don't worry, that's more than normal, even Leonardo Da Vinci was not very good at fractions, did you know?.

Read on!



Source: The A to Z of Mathematics: A Basic Guide




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