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how to turn a decimal into a fraction like the not so ...

Resolved Question:

how to turn a decimal into a fraction like the not so simple ones    0.444,0.625,0.523
Submitted: 10 years ago.
Category: Homework
Expert:  mathsmart replied 10 years ago.
Any terminating decimal can be turned into a fraction by putting the decimal over 1 with as many zeros as there are digits in the decimal.

For example:

.444 = 444/1000
.625 = 625/1000
.523 = 523/1000

Some of these can then be reduced. 444/1000 reduces to 111/250 by dividing the numerator and denominator each by 4.

So .444 = 111/250

625/1000 reduces to 5/8 by dividing the numerator and denominator both by 125 (you may need to do this in several steps), so

.625 = 5/8

523/1000 is not reducible, so that is the simplest fraction form of .523

You may also want to turn a repeating decimal into a fraction. This is a little bit harder. Here are two examples showing how to do it:

1) Turn .777... into a fraction

You need to do a little algebra here:

First let n = .777....
Multiplying by 10, we get 10n = 7.777...

Now we can subtract the first equation from the second to get:

10n - n = 7.777... - 0.777...

Beautifully, the repeating sevens cancel out on the right hand side and we get:

9n = 7

Dividing both sides by 9 gives us

n = 7/9

7/9 is the fraction equivalent of .777...

2) Find the fraction equivalent of .23232323....

This one is a little different because there are 2 digits that repeat instead of just one:

let n = 0.232323...

This time, because there are 2 digits, you multiply both sides by 100 to get:

100n = 23.232323...

Now we can subtract again to get

100n - n = 23.232323... - .232323...

99n = 23

n = 23/99

so 23/99 is the fraction equivalent to .232323...

Customer: replied 10 years ago.
Reply to mathsmart's Post: 0.444=111/250 is the answer we got but our answer key says 4/9. I am questioning this because this problem was given by a program we have titled math factory it's basic math for elementary school kids-- you showed us the algebraic way to do it. are you sure there is not a way for a basic elementary school child to know this (unbelievable)or calculate this. Is there a rule for rounding ex .66666 67% or does it stay 66% or does it depend on the instructors instructions
Expert:  mathsmart replied 10 years ago.

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mathsmart, Tutor
Category: Homework
Satisfied Customers: 909
Experience: BA in Math. Over six years experience in teaching and tutoring math and standardized test prep.