Question

Convert the following, repeating, decimal into a fraction in simplest form .17 repeating

Answer 1

To convert .17 repeating into a fraction, let's call it x:

x = .17 + .0017171717...
10x = 1.7 + .17171717...
Subtract the two equations:
10x - x = 1.7 + .17171717... - (.17 + .0017171717...)
9x = 1.70373737...
Now, let's subtract these two equations:
1000x - 10x = 1700 + 17.37373737... - (17 + 0.1707171717...)
990x = 1700 + 17.20302020...
Simplifying the equation:
990x = 1717.20302020...
Now, let's subtract these two equations:
10000x - 100x = 17170 + 17.20302020... - (1717 + 1.720302020...)
9900x = 15453.483180209...
Now, simplify the equation:
x = (15453.483180209...) / 9900

To find the simplest form of this fraction, you can simplify it further by dividing both the numerator and denominator by their greatest common divisor.