Question

If $0.116$ can be written as $\frac{a}{b}$ in the simplest form of fraction, then

• A. $a=29,b=250$
• B. $a=250,b=29$
• C. $a=29,b=500$
• D. $a=250,b=58$

Answer 1

The correct option is A $a=29,b=250$

Step 1: Rewrite the decimal as a fraction with a denominator of 1:
$\frac{0.116}{1}$

Step 2: The unit digit 6 is in thousandths place (0.116), so we place 116 over 1000 to create a equivalent fraction $\frac{116}{1000}.$

$\therefore \frac{0.116}{1}=\frac{116}{1000}$

Step 3: Simplify the fraction.
$\frac{116}{1000}=\frac{2\times 2\times 29}{2\times 2\times 250}$
Cancel out the common factors, we get
$=\frac{29}{250}$

$\therefore 0.116=\frac{29}{250}=\frac{a}{b}$
$\Rightarrow a=29,b=250$