repeating decimals

[vjackson]

Write the repeating decimal 0.456456 into a reduced fraction

 

[HallsofIvy]

Assuming it is the "456" that is repeating, writing x= 0.456456..., you can multiply by 1000 to get 1000x= 456.456456.... Notice that the two numbers have the same decimal part- because it is repeating that "456" just keeps coming. So if we subtract we get 100x- x= 99x= 456 and so $\displaystyle x= \frac{456}{999}= \frac{152}{333}$.

 

[Deleted member 4993]

Write the repeating decimal 0.456456 into a reduced fraction

For a quick review go to:

http://www.purplemath.com/modules/numtypes.htm

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.