SOLUTION: Please, assist me in this math problem. THANKS! Find fractional notation for each infinite sum. 0.454545... and 1.36666...

Click here to see ALL problems on Sequences-and-series

Question 84832: Please, assist me in this math problem. THANKS!
Find fractional notation for each infinite sum.
0.454545...
and
1.36666...
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Here's a way to do these:
1) Write 0.454545... as a fraction.
Let n = 0.454545... Multiply both sides by 100.
100n =45.454545... Subtract the first equation from the second equation.
99n = 45 Finally, divide both sides by 99
n = 45/99...but n = 0.454545..., so
0.454545...= 45/99 = 5/11

Check this on your calculator!
2) Write 1.3666... as a fraction.
Let n = 1.3666... Multiply both sides by 10.
10n = 13.666... Multiply both sides by 10 again.
100n = 136.666... Now subtract 10n from 100n
90n = 123 Finally divide both sides by 90.
n = 123/90...but n = 1.3666... so
1.3666... = 123/90 = 41/30

Check this on your calculator!