Write each of the following as a common fraction

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Write each of the following as a common fraction. a. 3.75 e. 5.5 b. 0.15 f. 4.483 c. 0.008 d. 1.16 g. 0.0003 h. 0.026 a. The common fraction for 3.75 is (Simplify your answer.) b. The common fraction for 0.15 is (Simplify your answer.) c. The common fraction for 0.008 is (Simplify your answer.) d. The common fraction for 1.16 is (Simplify your answer.) e. The common fraction for 5.5 is (Simplify your answer.) f. The common fraction for 4.483 is (Simplify your answer.) g. The common fraction for 0.0003 is (Simplify your answer.) h. The common fraction for 0.026 is (Simplify your answer.)

The Correct Answer and Explanation is:

Here are the correct answers written as simplified common fractions:

a. The common fraction for 3.75 is 15/4
b. The common fraction for 0.15 is 3/20
c. The common fraction for 0.008 is 1/125
d. The common fraction for 1.16 is 29/25
e. The common fraction for 5.5 is 11/2
f. The common fraction for 4.483 is 4483/1000
g. The common fraction for 0.0003 is 3/10000
h. The common fraction for 0.026 is 13/500

Explanation (300 words)

Converting decimals into common fractions involves expressing the decimal as a ratio of whole numbers and then simplifying the result if possible.

To convert a decimal to a fraction, follow these steps:

  1. Determine the place value of the last digit in the decimal. This tells you the denominator. For example, in 0.15, the 5 is in the hundredths place, so write 15/100.
  2. Remove the decimal point by rewriting the number as a fraction using powers of 10. For example, 3.75 = 375/100.
  3. Simplify the fraction by dividing both numerator and denominator by their greatest common factor (GCF). For instance, 375/100 can be simplified by dividing both terms by 25, resulting in 15/4.

Let’s go through a few examples:

  • 3.75 = 375/100. The GCF is 25. Divide numerator and denominator by 25 → 375 ÷ 25 = 15, 100 ÷ 25 = 4 → 15/4.
  • 0.15 = 15/100. GCF is 5 → 15 ÷ 5 = 3, 100 ÷ 5 = 20 → 3/20.
  • 0.008 = 8/1000. GCF is 8 → 8 ÷ 8 = 1, 1000 ÷ 8 = 125 → 1/125.
  • 1.16 = 116/100. GCF is 4 → 29/25.
  • 5.5 = 55/10 → divide by 5 → 11/2.
  • 4.483 = 4483/1000 (already simplified).
  • 0.0003 = 3/10000.
  • 0.026 = 26/1000 → divide by 2 → 13/500.

This method works for both terminating decimals and those with place values up to ten-thousandths.

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