Step 1: Identify the number of decimal places

The decimal 7.7584 has 4 decimal places.

Step 2: Multiply by the appropriate power of 10

Multiply by 10⁴ = 10000 to eliminate the decimal point.

7.7584 × 10000 = 77584

Step 3: Write as a fraction

Step 4: Simplify the fraction

Find the greatest common divisor (GCD) of 77584 and 10000.

GCD(77584, 10000) = 16

Divide both the numerator and denominator by the GCD: