To express 87.5% as a fraction in its simplest form, follow these steps:
1. Convert the percentage to a fraction:
- A percentage is a fraction out of 100, so 87.5% can be written as [tex]\(\frac{87.5}{100}\)[/tex].
2. Write 87.5 as a fraction:
- Since 87.5 is a decimal, we can express it as [tex]\(\frac{875}{10}\)[/tex]. This is because 87.5 is equivalent to 87.5/1, and multiplying the numerator and denominator by 10 removes the decimal.
3. Substitute this fraction into the previous step:
- Therefore, [tex]\(\frac{87.5}{100}\)[/tex] becomes [tex]\(\frac{\frac{875}{10}}{100} = \frac{875}{10 \times 100}= \frac{875}{1000}\)[/tex].
4. Simplify the fraction by finding the greatest common divisor (GCD) of 875 and 1000:
- The GCD of 875 and 1000 is 125.
5. Divide both the numerator and the denominator by their GCD:
- [tex]\(\frac{875}{1000}\)[/tex] simplified becomes [tex]\(\frac{875 ÷ 125}{1000 ÷ 125} = \frac{7}{8}\)[/tex].
Thus, 87.5% in fractional notation, simplified to its lowest terms, is [tex]\(\boxed{\frac{7}{8}}\)[/tex].
