Question

PLEASE ANSWER WILL GIVE 75 POINTS!!!!!

Answer 1

Answer:

$\frac{4}{33}$ and $\frac{1}{27}$

Step-by-step 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 = $\frac{12}{99}$ = $\frac{4}{33}$ ← in simplest form

-------------------------------------------------------

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 = $\frac{37}{999}$ = $\frac{1}{27}$ ← in simplest form