how do you rewrite 3.83 repeating as a simplified fraction

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06-09-2017
Mathematics

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how do you rewrite 3.83 repeating as a simplified fraction

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j69cochran j69cochran · Answer 1 · 2017-09-10T20:17:32+02:00

If the number is 3.8333333.... then

X=3.83333....
10X = 38.3333.....

10X - X
38.3333....
- 3.8333....
= 34.5
so 9X = 34.5
X = 34.5/9
Multiple both top and bottom by 2 to get rid of decimal.
69/18
Normalize it to get rid of improper fraction.
3 15/18
Simplify
3 5/6

If the number is 3.838383838383.... then
X = 3.83838383...
100X = 383.83838383...

100X - X = 99X
383.83838383...
3.83838383...
380

99X = 380
X = 380/99

X = 3 83/99