[ipushmycar]

Can anyone explain to me how to convert a repeating binary fraction to base 10?

For example, 0.1001100110011001... or 0.011011011011... my final is coming up and I need to know how to convert them. I know how to convert regular binary fractions to decimal just not repeating.

Thanks,
Ipush

[r.stiltskin]

Multiply the binary fraction by a power of 2 to give a result such that you can "cancel out" the repeating fraction by subtracting the original number. Remember, you can multiply a binary fraction by 2 just by shifting the decimal point 1 place to the right. For example:

Let x = .10011001...(binary)
2⁴ = 16 so

16x = 1001.10011001...(careful, here the left side is decimal, the right side is still binary)
__x =______.10011001...
15x = 1001
now it's easy to convert the right side to decimal, so
15x = 9

and you can easily finish by solving for x.