Multi-Part
Lesson
1
PART
B
NAME ________________________________________ DATE _____________ PERIOD _____
Enrich
Writing Repeating Decimals as Fractions
All fractions can be written as decimals that either terminate or repeat. You have
learned how to use a power of 10 to write a terminating decimal as a fraction.
Below, you will study a strategy to write a repeating decimal as a fraction.
For Exercises 1–4, write each fraction as a decimal. Use bar notation
if the decimal is a repeating decimal.
−
1
1. −
0.1
−
2
2. −
0.2
−
3
3. −
0.3
−
5
4. −
0.5
9
9
9
9
5. Describe the relationship between the numerator of each fraction and
its decimal equivalent.
The numerator is the same as the repeating part of the decimal.
For Exercises 6–9, write each fraction as a decimal. Use bar notation
if the decimal is a repeating decimal.
−−
0.07
−−
37
8. −
0.37
−−
0.24
−−
82
9. −
0.82
7
6. −
24
7. −
99
99
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
99
99
10. Describe the relationship between the numerator of each fraction and
its decimal equivalent.
The repeating part of the decimal is the same as the numerator,
with a zero added if the numerator is a single digit.
−−
11. Use the relationship from Exercise 10 to write the decimal 0.52 as a
fraction. Check your work using long division.
52
−
99
12. Using your observations from Exercises 5 and 10, make a prediction
127
. Check to see if your prediction
about the decimal equivalent of −
999
−−−
was correct by using long division. 0.127
4
4 4
13. How are the decimal equivalents of −
, − and − different? Explain.
9 99
999
They differ in the number of digits that repeat. Extra zeros
are added in front of the four depending on how many digits repeat.
For Exercises 14–19, write each decimal as a fraction. Check your
answers with a calculator.
−− 22
−−− 530
2
47
14. -0.47474747. . . - −
15. 0.22 −
=−
16. 0.530 −
99
9
999
99
3,266
−−−−
−−−−
10
328
17. -0.010010010. . . - − 18. 0.3266 −
19. 0.00328 −
999
9,999
99,999
17
Course 2 • Rational Numbers
012_024_NACRMC2C03_895160.indd 17
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11/25/09 11:05:13 AM