Question

Express 0.237 ( 37 bar) as the quotient of two integers having no common factors.​

Answer 1

The required form is $\dfrac{47}{18}$

Step-by-step explanation:

Given expression,

$0.2\bar{37}$

Let x = $0.2\bar{37}$,

⇒ x = 0.2373737373..............            ......(1)

Multiply by 100 both sides,

100x = 237.3737373..................         .......(2),

Multiply by 10 both sides on equation (1),

10x = 2.37373737................               ..............(3),

Equation (2) - equation (3),

90x = 235

$\implies x =\frac{235}{90}$

Since, HCF(90, 235) = 5,

$x=\frac{235\div 5}{90\div 5}=\frac{47}{18}$

Where, 47 and 18 are distinct integers.

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