COMMON FRACTIONS INTO
DECIMAL FRACTIONS

PROBLEMS 2

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Written calculation by division

13.  Show the decimal pattern that each fraction generates..

  13.   a)   1
3
 = 0.333333. . .   b)   1
9
 = 0.111111. . .
 
  13. c)    1 
11
 = .090909. . .   d)   1
6
 = 0.1666666. . .

14.  From your calculations in the previous problem, answer the
13.  following.

  14.  a)  Having calculated the decimal for  1
3
, write the decimal for  2
3
.

0.666666. . .

  14.  b)  Having calculated the decimal for  1
9
, write the decimal for  4
9
.

0.444444. . .

  14.  c)  Having calculated the decimal for   1 
11
, write the decimal for   2 
11
.

0.181818. . .

  14.  d)  Write the decimal for   3 
11
0.272727. . .
 
  14.  e)  Write the decimal for   7 
11
0.63636363. . .
  14.  f)  Having calculated the decimal for  1
6
, write the decimal for  5
6
.

0.8333333. . .


15.  30 minutes, as a fraction of an hour expressed as a decimal, is
15.  .5 hours.  What fraction of an hour, expressed as a decimal, is 35
15.  minutes?

  Since 60 minutes = 1 hour, then 35 minutes =  35
60
 of an hour.
  To express  35
60
 as a decimal, first reduce it to   7 
12
. (Lesson 22.)
  To express   7 
12
 as a decimal, divide 7 by 12, according to the

technique of Lesson 12. You will find:

 7 
12
 is approximately .583.

35 minutes are approximately .583 hours.

16.  How will you know when the pattern of digits repeats?

When the same remainder is repeated. Lesson 12.

  17.   The decimal for  1
7
 will not be exact.  Nevertheless, there will be a
  pattern to the digits.  What is that pattern?
1
7
= 0.142857 142857 142857. . .

Calculator problems

18.  Express each of the following as a decimal.  If the decimal is not
18.  exact, round it off to three decimal digits.  

  15.  a)   11
16
 = 0.6875   b)    7 
32
 = 0.21875
  15.  c)    8 
11
0.727   d)    22 
101
0.218

19.  a)  In a class of 37 students, 11 got B.  What fraction of the students

got B?    11
37

19.  b)  Express that fraction as a decimal.  (Round off to three decimal
13.  b)   digits.)  approximately .297

19.  c)  Express that decimal as a percent.  29.7%  15.

20.  Review of percent (Lesson 14)

20.  a)  How much is 9¼% of $68.50?  $6.34

20.  b)  $68.50 is 9¼% of how much?  $740.54

20   c)  12 is what percent of 26?  46.2%


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