Convert a small percent to a fraction: What fraction is equivalent to 2/5%? (Express in simplest form.)

Introduction / Context:Percent to fraction conversion requires dividing by 100. When the percent itself is a fraction (like 2/5%), divide that fraction by 100 to find the fraction of a whole. Then simplify to the lowest terms.

Given Data / Assumptions:We have 2/5%.

Concept / Approach:Convert percent to a pure fraction: (2/5)% = (2/5)/100 = 2 / 500. Simplify by dividing numerator and denominator by 2 to obtain 1/250.

Step-by-Step Solution:

Verification / Alternative check:As a decimal: 2/5% = 0.4% = 0.004. Fraction 1/250 = 0.004, confirming equivalence.

Why Other Options Are Wrong:1/40 = 2.5%; 1/125 = 0.8%; 1/500 = 0.2%; 2/25 = 8%. None match 0.4%.

Common Pitfalls:Forgetting the “per hundred” and treating 2/5% as 2/5 directly, or converting to 1/5 incorrectly.

Final Answer:1/250