Write 3.6% as a fraction in simplest form.
The correct answer and explanation is:
Correct Answer:
3.6% as a fraction in simplest form is 9/250.
Explanation (300 Words):
To convert 3.6% into a fraction in simplest form, follow these steps:
Step 1: Understand the meaning of percent
The term percent means “per hundred.” So: 3.6%=3.61003.6\% = \frac{3.6}{100}
Step 2: Eliminate the decimal
To remove the decimal from the numerator (3.6), multiply both the numerator and the denominator by 10: 3.6×10100×10=361000\frac{3.6 \times 10}{100 \times 10} = \frac{36}{1000}
Step 3: Simplify the fraction
Now, simplify the fraction 361000\frac{36}{1000}. Find the greatest common divisor (GCD) of 36 and 1000.
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
The GCD of 36 and 1000 is 4.
So divide numerator and denominator by 4: 36÷41000÷4=9250\frac{36 \div 4}{1000 \div 4} = \frac{9}{250}
Step 4: Final Answer
3.6%=92503.6\% = \frac{9}{250}
This is the simplest form because the numerator (9) and denominator (250) have no common factors other than 1.
Why this matters:
Converting percentages into fractions is useful in real-world applications like cooking, budgeting, and measuring. Fractions provide exact values, whereas percentages are sometimes rounded or estimated. Simplifying fractions makes them easier to understand and compare. For instance, if you’re calculating tax (3.6%) on an item, using the fraction 9250\frac{9}{250} might help in precise manual calculations.