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 as a fraction in lowest terms.

      A. . The three repeating digits are 126. Placing the 126 over a number with three 9’s, you reduce by dividing the numerator and denominator by 9.

      Q. Write the decimal as a fraction in lowest terms.

      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 Change to a decimal.

45 Change to a decimal.

      46 Change to a decimal.

      47 Change 0.45 to a fraction.

      48 Change to a fraction.

      49 Change to a fraction.

50 Round the decimal 4.172797 to the nearest thousandth.

Practice Question Answers and Explanations

      1 . First, divide the 29 by 8. The number 8 divides 29 three times with a remainder of 5.

      2 . Multiply the 4 and 9 and then add the 5, which equals 41. Then write the fraction with this result in the numerator and the 9 in the denominator.

      3 . Multiply the 4 times 100 and add the 7. Put the sum over 100.

      4 . Ignore the negative sign at first; you don’t want it involved in the computation. First multiply the 2 times 13 to get 26. Add the 1 to get 27. You have 27 in the numerator, 13 in the denominator, and now you put the negative sign in front.

      5 . The number 11 divides 402 a total of 36 times with 6 left over. The 36 goes in front, with the 6 in the numerator and 11 in the denominator. This example makes it especially apparent that the mixed number is more understandable.

      6 . Divide 7 into 19, for a quotient of 2. The remainder 5 goes in the numerator. Put the negative sign in front of the 2.

      7 . To get 28 in the denominator, multiply 7 by 4:

      8 . Multiply both the numerator and denominator by 5:

      9 . The number 4 is the greatest common divisor of 16 and 60 because and . So multiply by to get

      Or, if you prefer, divide both the numerator and denominator by 4:

      10 . The largest common divisor of 63 and 84 is 21, because and . So

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