What is 22.5% in a fraction in simplest form
The correct answer and explanation is:
Answer:
22.5% as a fraction in simplest form is 9/40.
Explanation:
Percentages are a way to express a number as a part of 100. The symbol “%” means “per hundred.” So, 22.5% literally means 22.5 out of 100.
Step 1: Write 22.5% as a fraction
First, convert the percentage to a fraction with denominator 100: 22.5%=22.510022.5\% = \frac{22.5}{100}
Since fractions are usually written with whole numbers in numerator and denominator, convert 22.5 to a whole number by multiplying numerator and denominator by 10: 22.5100=22.5×10100×10=2251000\frac{22.5}{100} = \frac{22.5 \times 10}{100 \times 10} = \frac{225}{1000}
So, 22.5% = 225/1000.
Step 2: Simplify the fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator (225) and denominator (1000).
- Factors of 225 include: 1, 3, 5, 9, 15, 25, 45, 75, 225
- Factors of 1000 include: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
The greatest common divisor is 25.
Step 3: Divide numerator and denominator by 25 2251000=225÷251000÷25=940\frac{225}{1000} = \frac{225 \div 25}{1000 \div 25} = \frac{9}{40}
Final simplified fraction:
22.5%=94022.5\% = \frac{9}{40}
Additional Notes:
- Converting percentages to fractions is useful because fractions can be manipulated more easily in mathematical operations.
- The decimal 22.5 can also be thought of as 22.5/100 = 0.225, which confirms that 9/40 = 0.225.
- This fraction, 9/40, cannot be simplified further because 9 and 40 share no common factors other than 1.
- Percentages can always be converted to fractions by dividing by 100 and then simplifying.