Repeating Decimals Worksheet Page 3
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1
2
3Exercise 1. The correct fractions are as follows:
0.36 =
0.46 =
0.56 =
0.76 =
0.86 =
0.96 =
1 1
7
1 7
2 3
1 3
2 9
3 0
1 5
3 0
3 0
1 5
3 0
The pattern can actually be seen more easily using a common denominator
of 30:
, , , , ,
11
14
17
23
26
29
30
30
30
30
30
30
3
is the difference from one fraction to the next, just as the decimals differ
30
by 0.1.
20
(You may wonder why
seems to be missing from the middle of the
30
sequence above; this is because
= =
, which has no delayed repetend.)
20
2
0.6
30
3
Exercise 2. The correct fractions and mixed numbers are as follows:
2.345 =
=
3.456 =
=
4.567 =
=
1 2 9
2
19
1711
3
226
2261
4
281
5 5
55
495
495
495
495
5.678 =
=
6.789 =
=
9 3 7
5
3361
6
391
112
1 6 5
165
495
495
Again, the patterns can be seen more easily by using a common
denominator of 495:
,
,
,
,
1161 1711
2261
2811 3361
(550 is the difference between numerators);
495
495
495
495
495
2
,3
, 4
,5
, 6
171
226
281
336
391
(55 is the difference between numerators).
55
495
495
495
495
Exercise 3. The easiest way to find one such fraction or mixed number is
simply to type in a decimal with the desired type of repetend. For example,
767
type “3.40888888...” [=]. The calculator outputs the fraction
(which, by
225
a Û
b
d
pressing [SHIFT]-[S D] (
), can be seen to be equal to the mixed
c
c
3
92
number
).
225
In general, the fractions that will work are those that have
denominators of 12, 36, 60, 75, 150, 180, 225, 300, 450, and 900 when
written in simplest form.
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