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How do I convert fractions into decimals?

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Pauline Sheehan eNotes educator | Certified Educator

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Converting fractions into decimals can be done easily if the concept behind decimals (or decimal fractions as they are also called) is understood.

Decimals work in quantities of tenths (0.1), hundredths (0.01), thousandths (0.001) and so on. For some fractions, it is a straightforward process to convert; for example, `1/10=0.1`

`2/10=0.2, 3/10=0.3` You can see the pattern. Similarly with hundredths: `1/100=0.001, 2/100 = 0.002, 3/100=0.003`  and so on.  Fractions that can be multiplied to make the denominator 100 can also be done by means of a quick calculation: `3/5=6/10 therefore 3/5=0.6` and `3/50= 6/100 therefore 3/50=0.06`

Quite often though, it is not possible to do these kind of calculations with denominators that do not easily convert to 10 or 100 or 1000; for example, `3/9` . Therefore, we divide 3 by 9 because, in fact the line in the fraction between the 3 and the 9 is a dividing line and means "divide". Take care not to do the division the wrong way around! We are dividing the numerator (the top) by the denominator (the bottom).

Using our example, we know that 9 does not go into 3 so we need to do 9 into 3.0000 as many times as we need because adding zeros after the decimal comma or point will not change the essence of the number 3. In other words` 3 = 3.0 = 3.00= 3.000` and so on. 

 Now we treat it like any division. 9 into 3 does not go so we will have an answer that starts 0.

Carry the 3 over the decimal point to the first zero so now we will do 9 into 30, which goes 3 times (remainder 3) as 9 x 3 =27. So now we have 0.3 and we carry the remainder of 3 to the next zero and we do 9 into 30 again. This answer will render a recurring decimal of 0.333 (continuing) so stop at 2 or 3 decimals depending on the question. 

Try another one, which is not a recurring decimal answer; for example, `5/8`  So we say, 5 divide by 8. Place several zeros after the decimal point; ie 5.0000 and start with 8 into 5 (doesn't go) so we will have an answer that starts with 0.

Now do 8 into 50 which goes 6 times (with a remainder of 2)  so we have 0.6 and we carry the remainder of 2 and do 8 into 20 which goes twice (remainder 4). So now we have 0.62. Carrying the remainder 4 to the next zero we get 8 into 40 which goes 5 times (exactly) so our final answer is `5/8 =0.625 .`

If we are dealing with mixed numbers such as `1 5/8` , we convert it to an improper fraction, in this case, of `13/8` and do the calculation in the same way, making the 13 into 13.000 (or as many zeros as we may need) such that 8 into 13 goes once so we have 1. and the remainder of 5 is carried to the zero and teh answer is `1.625` . Note how the decimal part of the answer is the same!    

Ans: To convert fractions to decimals divide the numerator by the denominator. 

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tjbrewer eNotes educator | Certified Educator

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Converting fractions into decimals is a relatively easy task.  A fraction is form of division.  You divide the numerator (the top number) by the denominator (the bottom number).  So `3/4=3-:4`

To make a fraction into a decimal you take the division it represents and set it up for long division `4|~3.` And you keep adding zeros into the dividend until you either get a remainder of zero, or you recognize a pattern resulting in a repeating decimal.  To carry our example to its conclusion:

`4|~bar3.00` four cannot go into 3, so that digit in the quotient is zero.  Four goes into 30, seven times, putting a 7 right behind the decimal point in the quotient.  4x7=28, we subtract 30-28=2.  We bring down the second zero and get 20.  Four goes into 20, 5 times, putting a five in the quotient.  4x5=20, remainder is zero. The quotient is .75, voila you just converted `3/4` into a decimal.  This works for any fraction.

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malkaam | Student

There is a very simple trick to convert fractions into decimals, once you know that, you can easily convert fractions into decimals.

Foremost, consider the fraction given. 

For example: the fraction is 35/100

Next, we see what is the denominator. we consider the number of zeroes in the denominator. 

Here, there are two zeroes.

Now, you add the decimal point, in such a way, that for each zero in the denominator you move the decimal in the numerator towards the left. 

Since we know that every number if doesn't include any decimals then there is always a decimal at the end. Here, the number 35 implies 35.0

So, since there are two zeroes in the denominator, we drag the decimal towards the left side, that is putting it two numerals towards the left.

So, the number would become 0.35

If you want me to further explain it in an easier way, and to explain the complicated cases as well, you can message me.  

acompanioninthetardis | Student

to convert fractions to decimals, simply divide the numerator with the denoiminator:

1/4= .25

3/9= .3333333


atyourservice | Student

Just divide and multiply by 100, for example if you have let say `1/2` just divide 17 by 2:

`1-:2=.5 `



another example will be