Algebra I All-in-One For Dummies. Mary Jane Sterling
Writing decimals as equivalent fractions
Decimals representing rational numbers come in two varieties: terminating decimals and repeating decimals. When changing from decimals to fractions, you put the digits in the decimal over some other digits and reduce the fraction.
Getting terminal results with terminating decimals
To change a terminating decimal into a fraction, put the digits to the right of the decimal point in the numerator. Put the number 1 in the denominator, followed by as many zeros as the numerator has digits. Reduce the fraction if necessary.
Q. Change 0.36 into a fraction.
A. There are two digits in 36, so the 1 in the denominator is followed by two zeros. Both 36 and 100 are divisible by 4, so the fraction reduces.
Q. Change 0.0005 into a fraction.
A. Don’t forget to count the zeros in front of the 5 when counting the number of digits. The fraction reduces.
Repeating yourself with repeating decimals
When a decimal repeats itself, you can always find the fraction that corresponds to the decimal. In this chapter, I only cover the decimals that show every digit repeating.
To change a repeating decimal (in which every digit is part of the repeated pattern) into its corresponding fraction, write the repeating digits in the numerator of a fraction and, in the denominator, as many 9’s as there are repeating digits. Reduce the fraction if necessary.
Q. Write the decimal
A.
Q. Write the decimal
A. The six repeating digits are put over six 9’s. Reducing the fraction takes a few divisions. The common factors of the numerator and denominator are 11, 13, 27, and 37. When completely reduced, you have
44
45 Change
46 Change
47 Change 0.45 to a fraction.
48 Change
49 Change
50 Round the decimal 4.172797 to the nearest thousandth.
Practice Question Answers and Explanations
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Or, if you prefer, divide both the numerator and denominator by 4:
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But let’s say you do this in two steps — both dividing by a common factor.
You see that both 63 and 84 are divisible by 7. So divide both the numerator