Write the rational number as the ratio of two integers in simplest form.
0.395959595...
detailed steps would be appreciated :)

Question

Write the  rational number as the ratio of two integers in simplest form.
0.395959595...
detailed steps would be appreciated :)

anonymous · Answer

0.95959595... = 95/99
0.0959595... = 95/99*(1/10) = 95 / 990
0.3 = 3/10
0.3959595... = 0.3 + 0.0959595 = 3/10 + 95/990 = 196/495

anonymous · Answer

why is it over 99?

anonymous · Answer

Anytime you have 0.something  and that something repeats you can put the pattern over 9s. The number of 9s you use depends on the length of the pattern.
For example
0.44444 = 4/9
0.182182182... = 182/999
0.418534185341853... = 41853/99999

nikvist · Answer

$$x=0.39595959...$$$$10x=3.9595959...$$$$1000x=395.95959...$$$$1000x-10x=395.95959...-3.9595959...$$$$990x=392$$$$x=\frac{392}{990}=\frac{196}{495}$$

anonymous · Answer

oh, also why did you multiply it by 1/10?

anonymous · Answer

A lot of people use @nikvist 's method too. That works, too.

anonymous · Answer

Because we want 0.0959595...not 0.959595.... To move the decimal, times by 1/0
0.3959595...is 0.3 + 0.095959595

anonymous · Answer

oh okay now i understand 
thank you for all the help