Step 1: Identify the number of decimal places

The decimal 0.09578 has 5 decimal places.

Step 2: Multiply by the appropriate power of 10

Multiply by 10⁵ = 100000 to eliminate the decimal point.

0.09578 × 100000 = 9578

Step 3: Write as a fraction

Step 4: Simplify the fraction

Find the greatest common divisor (GCD) of 9578 and 100000.

GCD(9578, 100000) = 2

Divide both the numerator and denominator by the GCD: