What is 17.5% as a fraction?

To convert 17.5% into a fraction, we can follow a straightforward process. Percentages are essentially fractions out of 100, so the first step is to express 17.5% as a fraction over 100.

Step-by-Step Conversion

Here’s how to do it:

1. Write 17.5% as a fraction: 17.5/100.
2. To eliminate the decimal, multiply both the numerator and the denominator by 10. This gives us: 175/1000.
3. Next, we simplify the fraction. To do this, we need to find the greatest common divisor (GCD) of 175 and 1000.

Finding the GCD

The GCD of 175 and 1000 can be found by listing the factors or using the Euclidean algorithm. However, in this case, we can see that both numbers are divisible by 25:

• 175 ÷ 25 = 7
• 1000 ÷ 25 = 40

Thus, we can simplify 175/1000 to 7/40.

Final Result

Therefore, 17.5% as a fraction is 7/40. This fraction is in its simplest form, meaning there are no common factors between the numerator and the denominator other than 1.

Understanding the Concept

To further grasp this concept, think of percentages as parts of a whole. When you say 17.5%, you're indicating that out of 100 equal parts, 17.5 parts are being considered. By converting it to a fraction, you're expressing that same idea in a different format, which can be useful in various mathematical contexts, such as calculations involving ratios or proportions.