Tiny percent of a large number: The number 0.05 is what percent of 20?

Difficulty: Easy

Correct Answer: 0.25%

Explanation:


Introduction / Context:
This is a ratio-to-percent conversion. We compare a small quantity (0.05) to a larger base (20) and then scale by 100 to express the relationship in percent terms. This is common in error rates and very low concentration problems.


Given Data / Assumptions:
Compute percent = (0.05 / 20) * 100%.


Concept / Approach:
Form the fraction of the part over the whole and multiply by 100. Ensure correct decimal manipulation because the numbers differ by orders of magnitude.


Step-by-Step Solution:

(0.05 / 20) * 100% = (0.05 * 100) / 20 % = 5 / 20 % = 0.25%


Verification / Alternative check:
As a decimal, 0.25% = 0.0025. 0.0025 * 20 = 0.05, which confirms the calculation.


Why Other Options Are Wrong:
2.5% corresponds to 0.5/20; 25% corresponds to 5/20; 0.025% and 0.5% are off by factors of 10 or 2 relative to 0.25%.


Common Pitfalls:
Forgetting to multiply by 100 to convert to percent or misplacing the decimal point during division.


Final Answer:
0.25%

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion