- Convert a percentage \(P\%\) to a fraction by writing \(\frac{P}{100}\) and simplifying it to its lowest terms.
- Convert a percentage to a decimal by dividing the value \(P\) by 100 (moving the decimal point two places to the left).
- The results are:
- a) \(45\% = \frac{9}{20} = 0.45\)
- b) \(37.5\% = \frac{3}{8} = 0.375\)
- c) \(12.5\% = \frac{1}{8} = 0.125\)
- d) \(66.66\% = \frac{3333}{5000} = 0.6666\)
- e) \(150\% = \frac{3}{2} = 1.5\)
- f) \(0.8\% = \frac{1}{125} = 0.008\)
Explanation
- Understanding the Conversion Process
To convert a percentage \(P\%\) to a decimal, we divide the percentage value \(P\) by 100, which is equivalent to shifting the decimal point two places to the left. To convert to a fraction, we write the percentage as \(\frac{P}{100}\) and simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD). For cases where \(P\) is a decimal, we first multiply both the numerator and denominator by a power of 10 to eliminate the decimal before simplifying.
- Step-by-Step Conversion of Percentages
For each percentage, we perform the conversions:
A\(45\% = \frac{45}{100} = \frac{9 \times 5}{20 \times 5} = \frac{9}{20}\). As a decimal, \(45 \div 100 = 0.45\).
B\(37.5\% = \frac{37.5}{100} = \frac{375}{1000}\). The GCD of 375 and 1000 is 125, so \(\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}\). As a decimal, \(37.5 \div 100 = 0.375\).
C\(12.5\% = \frac{12.5}{100} = \frac{125}{1000}\). The GCD of 125 and 1000 is 125, so \(\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}\). As a decimal, \(12.5 \div 100 = 0.125\).
D\(66.66\% = \frac{66.66}{100} = \frac{6666}{10000}\). The GCD of 6666 and 10000 is 2, so \(\frac{6666 \div 2}{10000 \div 2} = \frac{3333}{5000}\). As a decimal, \(66.66 \div 100 = 0.6666\). Note that if the intention was to represent the recurring decimal \(66.\bar{6}\%\), the exact fraction would be \(\frac{2}{3}\).
E\(150\% = \frac{150}{100} = \frac{15}{10} = \frac{3}{2}\). As a decimal, \(150 \div 100 = 1.5\).
f) \(0.8\% = \frac{0.8}{100} = \frac{8}{1000}\). The GCD of 8 and 1000 is 8, so \(\frac{8 \div 8}{1000 \div 8} = \frac{1}{125}\). As a decimal, \(0.8 \div 100 = 0.008\).
- Conclusion
The converted values are:
A\(45\% = \frac{9}{20} = 0.45\)
B\(37.5\% = \frac{3}{8} = 0.375\)
C\(12.5\% = \frac{1}{8} = 0.125\)
D\(66.66\% = \frac{3333}{5000} = 0.6666\)
E\(150\% = \frac{3}{2} = 1.5\)
f) \(0.8\% = \frac{1}{125} = 0.008\)
The final results for the fractions and decimals are summarized above.
Examples
Understanding how to convert percentages is crucial in everyday life. For instance, if a store offers a 37.5% discount on an item, recognizing this as \(\frac{3}{8}\) of the original price makes it easier to calculate the savings mentally. Similarly, knowing that 150% of a value is \(\frac{3}{2}\) times that value helps in managing budgets or calculating interest rates in financial planning. These conversions turn complex percentages into simpler numerical operations.