how would I turn .29292929 into a fraction. multiply by 100... then what?

Question

how would I turn .29292929 into a fraction.  multiply by 100... then what?

unklerhaukus · Answer

oh wait you mean
$$0.\dot2\dot9$$

anonymous · Answer

.29 repeating yes

unklerhaukus · Answer

yeah multiply by 100 is right,
then take away the original,,
you'll have 99 (original )=29

anonymous · Answer

what do you mean? take away the original?

sburchette · Answer

You can use a geometric series and then find the fraction that it converges to.

unklerhaukus · Answer

so
$$x=0.\dot2\dot9$$
$$100x=29.\dot2\dot9$$
$$99x=29$$
$$x=29/99$$
 $$0.\dot2\dot9=29/99$$

anonymous · Answer

why'd you subtract 1 though?

anonymous · Answer

anyone?

anonymous · Answer

@gd0x simply to get rid of nasty repeating parts

anonymous · Answer

@gd0x when you do calculation 100x-x we get rid of repeating parts from the decimal

anonymous · Answer

ohhhhh. got it got it.  ty

unklerhaukus · Answer

we are subtracting x

sburchette · Answer

.292929... = .29+.0029+.000029+...=(29/100)+(29/10000)+(29/1000000)+...
$$\sum_{n=1}^{\infty}(29/100^n)$$$$29\sum_{n=1}^{\infty}(1/100)^n$$This is a geometric series whose common ratio is (1/100) which is less than 1, thus it converges at $$a_1/(1-r)$$$$29[(1/100)/(1-(1/100)]$$$$29[(1/100)/(99/100)]$$$$29(1/99)$$$$29/99$$

anonymous · Answer

@SBurchette your method is awesome but i remember i used to solve these questions in the 6th or 7th standard & at that level Geometric Progression will go out of the beyond.