Question

PLEASE ANSWER WILL GIVE 75 POINTS!!!!!

Answer 1

`(4)/(33)` and
`(1)/(27)`

Explanation:

We require 2 equations with the repeating numbers placed after the decimal point.

let x = 0.1212...... (1) ← multiply both sides by 10

100x = 12.1212.... (2)

subtract (1) from (2) thus eliminating the repeating numbers

99x = 12 ( divide both sides by 99 )

x =
`(12)/(99)` =
`(4)/(33)` ← in simplest form

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let x = 0.037037....... (1) ← multiply both sides by 1000

1000x = 37.037037..... (2)

subtract (1) from (2) to eliminate the repeating numbers

999x = 37 ( divide both sides by 999 )

x =
`(37)/(999)` =
`(1)/(27)` ← in simplest form