Answer:
The required number in the fraction is x=11
Step-by-step explanation:
Given : The repeating decimal, 0.27..., is converted to the fraction [tex]0.27....=\frac{3}{x}[/tex]
To find : What is the value for x in the fraction ?
Solution :
Let [tex]y=0.272727...[/tex] ....(1)
Multiply both side by 100,
[tex]100y=27.2727...[/tex] .....(2)
Subtract (1) and (2),
[tex]100y-y=(27.2727....)-(0.272727...)[/tex]
[tex]99y=27[/tex]
[tex]y=\frac{27}{99}[/tex]
[tex]y=\frac{3}{11}[/tex]
On comparing with [tex]0.27....=\frac{3}{x}[/tex]
The value of x is 11.
Therefore, The required number in the fraction is x=11.
