Question

The decimal number $0.\overline{037}$ when converted to rational number form is

• A. 1/18
• B. 5/18
• C. 1/27
• D. 5/27

Answer 1

The correct option is C 1/27

Given:
$0.\overline{037}$ = 0.037037..
Let,x = 0.037037.. - Equation 1
10x = 0.37037... - Equation 2
100x = 3.7037.... - Equation 3
1000x = 37.037.. - Equation 4
Subtracting Equation1 from Equation 4, we have:

1000x - 1x = 37.037.. - 0.037037..
$⟹$ 999x = 37
$⟹$ x = $\frac{37}{999}$

$⟹$ x = $\frac{1}{27}$

$\therefore$ In rational number form, $0.\overline{037}$ = $\frac{1}{27}$