Convert reapeating decimal where all numbers do not repeat(expert) explain! 13 (3 has a line above it)

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Step-by-step explanation:

The bar above the 3 indicates the 3 is being repeated, that is

0.13333....

We require to make 2 equations with the repeating 3 after the decimal point.

let x = 0.13333... , then multiply both sides by 10 then 100

10x = 1.3333 ← equation with repeating 3 after the decimal point

100x = 13.3333 ← second equation with repeated 3 after the decimal point

Subtracting the equations eliminates the repeated 3, that is

100x - 10x = 13.333 - 1.333

90x = 12 ( divide both sides by 90 )

x = ← divide numerator/denominator by 6, hence

0.1333... =

2/15

Step-by-step explanation:

This is a mixed repeating decimal (only 3 us repeated but not the 1)

13-1: 90 =     12/90 = 2/15

you take the whole decimal(13) and then you subtract the non repeating decimal(1).This is the nominator

Then  on the denominator, for each repeating decimal you put a 9 and for each non repeating decimal you put a 0

denominator:90

details

step-by-step explanation: