Convert the decimal expansion 0.370370... to a fraction.

2 answers:

7 0

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 $\dfrac{10}{27}$

6 0

The answer is A 10/27 is 0.370370..

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