Step 1: Identify the number of decimal places

The decimal 7.829 has 3 decimal places.

Step 2: Multiply by the appropriate power of 10

Multiply by 10³ = 1000 to eliminate the decimal point.

7.829 × 1000 = 7829

Step 3: Write as a fraction

Step 4: Simplify the fraction

Find the greatest common divisor (GCD) of 7829 and 1000.

GCD(7829, 1000) = 1

Divide both the numerator and denominator by the GCD: