3C Decimal and Fraction Conversions

How about fraction and decimal conversions? We saw in the last chapter that we can convert a fraction into a decimal just by dividing the numerator by the denominator. Remember the denominator is the divisor, so it must go on the outside of the long division.

Also remember that some fractions convert into repeating decimals. Look at the example of 2/11. We just need to divide 2 by 11.

$$\begin{array}{cc}& 0.181818\\ 11& 2.000000\\ & -11\\ & 90\\ & -88\\ & 20\\ & -11\\ & 90\end{array}$$

Notice 2/11 = 0.18181818… = $0.\overline{18}$ Remember to put a bar over the repeating part. Note: 2/11 is not 0.18 or 0.1818 since these are terminating decimals. 2/11 is equivalent to an infinitely repeating decimal. Similarly the fraction 1/3 is not 0.3, 0.33 or 0.333. These decimals terminate. 1/3 = 0.333333333… = $0.\overline{3}$ Remember the bar over the number means that those digits continue forever.

Converting mixed numbers into decimals is not much more difficult than converting proper fractions into decimals. For positive mixed numbers, the whole part is the same as the digits to the left of the decimal point. So just convert the fraction part into a decimal and add it to the whole part.

For example suppose we want to convert the mixed number $9⁤\frac{3}{5}$ into a decimal. Notice 3/5 means $3÷5$. If we divide 3 by 5, remember the number dividing by goes on the outside of the long division. So we get the following. Notice 3/5 is the same as 0.6 as a decimal.

$$\begin{array}{cc}& .6\\ 5& 3.0\\ \multicolumn{2}{c}{-30}\\ \multicolumn{2}{c}{0}\end{array}$$

Now the whole part of the mixed number 9 is the same as the digit to the left of the decimal. So $9⁤\frac{3}{5}=9+\frac{3}{5}=9+0.6=9.6$

Try the following examples with your instructor.

What about converting a decimal into a fraction? Decimal to fraction conversions stem from the idea of understanding decimal places. Remember 0.7 means 7 tenths since it ends in the tenths place. So 0.7 = 7/10. When we write a fraction, we are often asked to write our answer in simplest form. Notice 7/10 is in simplest form since there is no positive whole-number factor greater than 1 that divides both 7 and 10. What about converting 0.024 into a fraction? The decimal ends in the thousandths place so 0.024 = 24/1000. Dividing the numerator and denominator by 8 gives us the simplest form of 3/125.

Try these examples with your instructor also.

Practice Problems Section 3C

Convert the following fractions and mixed numbers into decimals. Don’t forget to put a bar over any repeating parts.

1. $$\frac{3}{4}$$

   Check answer

   0.75

2. $$\frac{7}{16}$$

3. $$\frac{2}{9}$$

   Check answer

   $$0.\overline{2}$$

4. $$\frac{1}{20}$$

5. $$\frac{5}{6}$$

   Check answer

   $$0.8\overline{3}$$

6. $$\frac{7}{9}$$

7. $$\frac{7}{8}$$

   Check answer

   0.875

8. $$\frac{3}{32}$$

9. $$\frac{5}{18}$$

   Check answer

   $$0.2\overline{7}$$

10. $$\frac{7}{18}$$

11. $$\frac{11}{25}$$

    Check answer

    0.44

12. $$\frac{13}{16}$$

13. $$\frac{5}{7}$$

    Check answer

    $$0.\overline{714285}$$

14. $$\frac{16}{33}$$

15. $$\frac{7}{36}$$

    Check answer

    $$0.19\overline{4}$$

16. $$\frac{17}{80}$$

17. $$\frac{17}{18}$$

    Check answer

    $$0.9\overline{4}$$

18. $$\frac{11}{72}$$

19. $$9⁤\frac{1}{2}$$

    Check answer

    9.5

20. $$6⁤\frac{1}{5}$$

21. $$9⁤\frac{2}{3}$$

    Check answer

    $$9.\overline{6}$$

22. $$3⁤\frac{1}{8}$$

23. $$5⁤\frac{4}{15}$$

    Check answer

    $$5.2\overline{6}$$

24. $$1⁤\frac{5}{18}$$

25. $$14⁤\frac{7}{32}$$

    Check answer

    14.21875

26. $$2⁤\frac{1}{12}$$

27. $$20⁤\frac{4}{7}$$

    Check answer

    $$20.\overline{571428}$$

28. $$16⁤\frac{3}{32}$$

29. $$11⁤\frac{1}{15}$$

    Check answer

    $$11.0\overline{6}$$

30. $$9⁤\frac{32}{33}$$

Convert the following decimals into fractions or mixed numbers in simplest form.

31. 0.75

    Check answer

    $$\frac{3}{4}$$

32. 0.07

33. 0.6

    Check answer

    $$\frac{3}{5}$$

34. 0.005

35. 0.24

    Check answer

    $$\frac{6}{25}$$

36. 0.066

37. 0.13

    Check answer

    $$\frac{13}{100}$$

38. 0.048

39. 0.35

    Check answer

    $$\frac{7}{20}$$

40. 0.0018

41. 0.078

    Check answer

    $$\frac{39}{500}$$

42. 0.42

43. 0.00026

    Check answer

    $$\frac{13}{\mathrm{50,000}}$$

44. 0.092

45. 0.85

    Check answer

    $$\frac{17}{20}$$

46. 0.0054

47. 0.128

    Check answer

    $$\frac{16}{125}$$

48. 0.032

49. 14.5

    Check answer

    $$14⁤\frac{1}{2}$$

50. 8.25

51. 9.72

    Check answer

    $$9⁤\frac{18}{25}$$

52. 6.084

53. 20.38

    Check answer

    $$20⁤\frac{19}{50}$$

54. 13.8

55. 4.0002

    Check answer

    $$4⁤\frac{1}{\mathrm{5,000}}$$

56. 7.065

57. 5.44

    Check answer

    $$5⁤\frac{11}{25}$$

58. 136.99

59. 2.0055

    Check answer

    $$2⁤\frac{11}{2000}$$

60. 14.828

61. 9.62

    Check answer

    $$9⁤\frac{31}{50}$$

62. 44.076

63. 16.033

    Check answer

    $$16⁤\frac{33}{\mathrm{1,000}}$$

Adapted from Preparing for Algebra and Statistics, Third Edition, by Matt Teachout. License: CC BY 4.0. Copyright and sources.