Step 1: Identify the number of decimal places

The decimal 7.77164 has 5 decimal places.

Step 2: Multiply by the appropriate power of 10

Multiply by 10⁵ = 100000 to eliminate the decimal point.

7.77164 × 100000 = 777164

Step 3: Write as a fraction

Step 4: Simplify the fraction

Find the greatest common divisor (GCD) of 777164 and 100000.

GCD(777164, 100000) = 4

Divide both the numerator and denominator by the GCD: