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Question 474405: http://imageshack.us/photo/my-images/809/page656.jpg/
Thank you for spend time do my home work
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a reference that looks like it can be used to find the solution to your problem.
http://www.basic-mathematics.com/converting-repeating-decimals-to-fractions.html
your first number is .27 repeating endlessly.
put that number to the left of the decimal place to get 27.27
in order to do that you had to multiply the original number by 100.
your modified equation is 100x = 27.27
your equation is x = .27...
subtract x from 10x to get:
100x - x = 27.27... - .27...
combine like terms on both sides of this equation to get:
99x = 27
divide both sides of this equation by 99 to get x = 27/99.
reduce this equation to its simplest terms to get x = 3/11.
that should be your fraction.
use your calculator to see that 3/11 = .27272727...
the ... means that the 27 repeats endlessly.
it works !!!.
solving your second problem should be just as easy.
your second problem is .256...
the repeating digits are 256.
put them to the left of the decimal point to get 256.256...
in order to do that, you had to multiply .256 by 1000, so your equations are:
x = .256...
1000x = 256.256...
subtract x from 1000x to get:
1000x - x = 256.256... - .256...
combine like terms to get:
999x = 256
divide both sides of this equation by 999 to get:
x = 256/999
user your calculator to show that 256/999 = .256256256...
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