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