Express \(0.1\overline7\) in the form \(\frac{p}{q}\), where p and q are integers and q ≠ 0.

Question

Question

This question was previously asked in

RRB Group D 9 Sept 2022 Shift 3 Official Paper

Answer 1

Given:

Express \(0.1\overline7\) in the form \(\frac{p}{q}\), where p and q are integers and q ≠ 0.

Concept used:

All the numbers that can be converted to p/q form where p, q are integers and q ≠ 0, are called rational numbers.

Calculation:

Let's suppose,

x = 0.1777… —(1)

So, 10x = 1.777… —(2)

Subtract (2) from (1), we get,

⇒ 10x - x = 1.777 - 0.1777

⇒ 9x = 1.6 x = \(1.6\over 9\)

⇒ x = \(16\over 90\)

⇒ \(x = {p\over q} = {8\over45}\)

Hence, 'Option 4' is correct.

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