8th Grade Math
5.1 Homework: Rational Numbers
Name:__________________________________
Period: ____
Write the following fractions as decimals. MEMORIZE THEM. They are Benchmark Factions.
Next, graph them on the number line, labeling each one. It’s important to know where they are.
1)
1
4
= _____
6)
1
8
2)
1
2
= _____
= _____
7)
3
8
3)
3
4
= _____
= _____
8)
5
8
4)
1
3
= _____
= _____
9)
7
8
5)
2
3
= _____
= _____
10.
Graph each pair of numbers on the number line. Use the graph and write , , or  to compare the
numbers. Example:
11.
1.7
12.
0.09
13.
4.34
14.
11
15.
3.8
3
16.
1
3
4
8
16
0.65
4
5
Convert each fraction to a decimal, then determine if it’s decimal expansion is repeating or
terminating. Transfer your answer to the table under the corresponding title.
Example:
17.
22.
27.
1
25
7
= 0.04
18.
9
1
23.
3
2
28.
9
5
12
7
6
2
5
Terminating Decimal (it ends).
19.
24.
29.
5
8
5
99
3
8
13
20.
16
3
25.
26.
4
30 =
21.
1
4
31.
8
11
2
3
125
999
Repeating Decimals
Terminating Decimals
(those that repeat forever)
(those that end)
Fraction
Decimal
Fraction
1
25
Decimal
0.04
32. Look at the “Repeating Decimals” in the table above and their corresponding fractions. List the
denominators of the fractions that are repeating decimals. What is similar about these denominators?
33. Google “What makes a repeating decimal repeat”, read the Wikipedia definition and describe which
denominators will produce repeating decimals.
Convert the following terminating decimals to fractions. Reduce to lowest terms.
34. 2.11
35. 0.345
36. - 0.75
37. 0.6
38. 0.125
39. 3.5
40. 5
41. 0.09
Decimals that repeat are also rational numbers. Follow these steps, and study the examples
carefully to change each repeating decimal to a fraction.
Step 1: Let 𝑥 equal the repeating decimal.
Step 2: Multiply by powers of 1, 10, or 100 to create 2 equations that isolate the repeating part
of the decimal.
Step 3: Subtract the equations to remove the repeating part of the decimal.
Step 4: Solve the resulting equation and simplify the fraction.
Let 𝑥 = 0.333 …
Let 𝑥 = 0.1666 …
10𝑥 = 3.333 …
− 1𝑥 = 0.333 …
9𝑥 = 3
𝟑
𝟏
𝒙=
=
𝟗
𝟑
100𝑥 = 16.666 …
− 10𝑥 = 1.666 …
90𝑥 = 15
15 1
𝒙=
=
90 6
Convert each repeating decimal to a fraction. Show all steps. Reduce to lowest terms.
42.
0.444 …
43.
0.1222…
45.
0. 6̅
46. 0.151515….
44.
̅
0.05
47. 0.0707…
Just for Fun:
We have practiced converting decimals to fractions (see above). Now try
converting this never-ending decimal to a fraction (hint: it does not repeat).
0.34307856940820…
5.1 Odd Answers
1. 0.25
3. 0.75
̅
5. 0.6
7. 0.375
9. 0.875
̅
17. 0.7
35.
19. 0.625
37.
̅̅̅̅
21. 0.72
̅
23. 0.16
39.
41.
25. 0.75
̅
27. 0.2
29. 0.375
̅̅̅̅̅
31. 0.125
33. Look it up 
43.
45.
47.
69
200
3
5
7
2
9
100
11
90
2
3
7
99