Verified Answer :

  • To convert a percentage to a decimal, divide by 100.
  • To convert to a fraction, place the value over 100 and simplify.
  • The resulting values are: a) \(\frac{9}{20}, 0.45\); b) \(\frac{3}{8}, 0.375\); c) \(\frac{1}{8}, 0.125\); d) \(\frac{3333}{5000}, 0.6666\); e) \(\frac{3}{2}, 1.5\); f) \(\frac{1}{125}, 0.008\).
  • \(\boxed{a) \frac{9}{20}, 0.45; b) \frac{3}{8}, 0.375; c) \frac{1}{8}, 0.125; d) \frac{3333}{5000}, 0.6666; e) \frac{3}{2}, 1.5; f) \frac{1}{125}, 0.008}\)

Explanation

  1. Analysis and Methodology

To convert a percentage to a decimal, we divide the percentage value by 100. For example, \(x\% = \frac{x}{100} = 0.x\). To convert a percentage to a fraction, we express it as \(\frac{x}{100}\) and simplify the resulting fraction by dividing the numerator and the denominator by their greatest common divisor. We will apply these steps to each of the given values: \(45\%\), \(37.5\%\), \(12.5\%\), \(66.66\%\), \(150\%\), and \(0.8\%\).

  1. Calculations and Simplification
A\(45\% = \frac{45}{100} = 0.45\). Simplifying the fraction: \(\frac{45 \div 5}{100 \div 5} = \frac{9}{20}\).
B\(37.5\% = \frac{37.5}{100} = 0.375\). Simplifying the fraction: \(\frac{37.5}{100} = \frac{375}{1000} = \frac{375 \div 125}{1000 \div 125} = \frac{3}{8}\).
C\(12.5\% = \frac{12.5}{100} = 0.125\). Simplifying the fraction: \(\frac{12.5}{100} = \frac{125}{1000} = \frac{125 \div 125}{1000 \div 125} = \frac{1}{8}\).
D\(66.66\% = \frac{66.66}{100} = 0.6666\). The fraction form \(\frac{66.66}{100} = \frac{6666}{10000}\). Simplifying: \(\frac{6666 \div 2}{10000 \div 2} = \frac{3333}{5000}\).
E\(150\% = \frac{150}{100} = 1.5\). Simplifying the fraction: \(\frac{150 \div 50}{100 \div 50} = \frac{3}{2}\).

f) \(0.8\% = \frac{0.8}{100} = 0.008\). Simplifying the fraction: \(\frac{0.8}{100} = \frac{8}{1000} = \frac{8 \div 8}{1000 \div 8} = \frac{1}{125}\).

  1. Conclusion

The conversions for each percentage are summarized as follows:

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) \(0.8\% = \frac{1}{125} = 0.008\)
These values represent the exact decimal and simplest fractional forms of the given percentages.

Examples

Percentages are frequently used in everyday life, such as calculating discounts, tax rates, or interest. For example, if a store offers a \(37.5\%\) discount on an item originally priced at \(\$80\), you can easily calculate the discount amount by using the fractional form \(\frac{3}{8}\): \(80 \times \frac{3}{8} = 10 \times 3 = \boxed{\$30}\). Knowing how to convert between percentages, fractions, and decimals allows you to perform these mental calculations quickly and accurately.

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