Answer:
[tex]0.370370.....=\dfrac{10}{27}[/tex]
A is correct
Step-by-step explanation:
We are given a repeating decimal 0.370370.......
Let,
[tex]x=0.\overline{370}[/tex]
[tex]x=0.370370370...[/tex]
In the given repeating decimal 3 digits repeating.
[tex]x=0.370370370.....--------(1)[/tex]
So, we will multiply both sides by 1000
[tex]1000x=370.370370370.....-------(2)[/tex]
Subtract eq(2) - eq(1)
[tex]1000x-x = 370[/tex]
[tex]999x=370[/tex]
[tex]x=\dfrac{370}{999}[/tex]
Reduce the fraction by factor of 37
[tex]x=\dfrac{10}{27}[/tex]
Hence, The given repeating decimal 0.370370....... as fraction [tex]\dfrac{10}{27}[/tex]
