Answer:
[tex]\frac{4}{33}[/tex] and [tex]\frac{1}{27}[/tex]
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 = [tex]\frac{12}{99}[/tex] = [tex]\frac{4}{33}[/tex] ← 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 = [tex]\frac{37}{999}[/tex] = [tex]\frac{1}{27}[/tex] ← in simplest form