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what if a zero is at the end of a decimal and you try to convert it to a fraction?

here is an example- 0.05 would that convert to 5/100 or 50/100 or 5/10?

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2 Answers

A method that always works is the following. Let x equal your decimal, in this case x = 0.05. Now what do you have to do to this equation to eliminate the decimal? In our case, multiply both sides by 100, so

     100*x = 5

Thus, x is 5/100, or 1/20, whichever form suits your purpose.

Sometimes, the method is a little tricky. For example, suppose the decimal is the infinite string 0.33333... In this case, my equation is x = 0.333333... If I multiply both sides by 3, the equation becomes

    3*x = 0.9999999...

Now the trick is you need to know that 0.999999.... is just another way of writing 1. So the equation is really 3*x = 1, and x = 1/3.


For the repeating decimal cases you can multiply by the repeating cycle's length and do a subtracton to get a problem with a terminating decimal. Ex: x=1.8[3] (the threes repeat). Then:

10x=18.[3] or 18.3[3] if you wish. so 10x-x=16.5=9x so 90x=165 or x=165/90=11/6.

When converting decimals to fractions without the use of a scientific calculator the easiest thing to do is think of it in terms of money. So for your example 0.05 would be 5 cents out of a hundred 0r 5/100. If it was 0.5 it would be 50 cents or 5/10 . Each space after the decimal point is a mutiple of ten so first is 1/10 then 1/100 then 1/1000 and so on. Hope this helps you.