Question

Simplify $1.\overline{24}$ as an improper fraction.

• A. 123/90
• B. 41/33
• C. 91/90
• D. 124/99

Answer 1

Answer:

B. 41/33

The final simplified value is $\frac{41}{33}$.

1: Write the repeating decimal as an equation

Let $x = 1.242424...$ — (Equation 1)

2: Multiply to shift the repeating block

Since there are two repeating digits under the bar (2 and 4), multiply both sides of the equation by 100:
$100x = 124.242424...$ — (Equation 2)

3: Subtract Equation 1 from Equation 2

Subtracting the equations eliminates the infinite repeating decimal part:
$100x - x = 124.242424... - 1.242424...$
$99x = 123$

4: Solve for $x$ and reduce to lowest terms

$x = \frac{123}{99}$

Divide both the numerator and the denominator by their greatest common divisor, which is 3:

• $123 \div 3 = 41$

• $99 \div 3 = 33$

This gives the final improper fraction: $\frac{41}{33}$.