1. What Does 42.5% As A Fraction Mean?

Converting 42.5% to a fraction means expressing the percentage value as a ratio of two integers. Percentages are essentially fractions with a denominator of 100, so we start by writing 42.5 over 100.

2. Conversion Steps Explained

The conversion process involves these steps:

Detailed Steps:

1. Write the percentage as a fraction with denominator 100
2. Multiply numerator and denominator by 10 to eliminate decimal
3. Simplify by dividing numerator and denominator by 25 (GCD of 425 and 1000)
4. Final simplified fraction is 17/40

3. Practical Applications

Usage: This conversion is useful in probability calculations, statistics, and whenever fractional representation is preferred over percentages.

4. Verification Method

How to Verify: Convert 17/40 back to percentage (17 ÷ 40 × 100 = 42.5%) to confirm the conversion is correct.

5. Frequently Asked Questions (FAQ)

Q1: Why multiply by 10 in step 2?
A: To eliminate the decimal in the numerator (42.5 × 10 = 425).

Q2: How was the GCD of 25 determined?
A: The greatest common divisor of 425 and 1000 is 25 (425 ÷ 25 = 17, 1000 ÷ 25 = 40).

Q3: Can this fraction be simplified further?
A: No, 17 is a prime number and doesn't divide evenly into 40.

Q4: What's the decimal equivalent?
A: 17 ÷ 40 = 0.425, which matches our original percentage (0.425 × 100 = 42.5%).

Q5: When would I use the unsimplified form?
A: The 425/1000 form might be useful when working with thousandths or when the denominator needs to match other fractions in a calculation.