Step 1: Identify the number of decimal places

The decimal 47.7564 has 4 decimal places.

Step 2: Multiply by the appropriate power of 10

Multiply by 10⁴ = 10000 to eliminate the decimal point.

47.7564 × 10000 = 477564

Step 3: Write as a fraction

Step 4: Simplify the fraction

Find the greatest common divisor (GCD) of 477564 and 10000.

GCD(477564, 10000) = 4

Divide both the numerator and denominator by the GCD: