THE SET OF REAL NUMBERS
RATIONAL
INTEGERS
WHOLE
COUNTING
IRRRATIONAL
INDEPENDENT PRACTICE: STATE WHETHER THE FOLLOWING NUMBERS ARE RATIONAL
OR IRRATIONAL. (SIMPLIFY BEFORE MAKING THE DECISION.)
IF RATIONAL, STATE THE OTHER SET(S) IN WHICH THE NUMBER BELONGS.
1.
𝟐
2. 𝟓
𝟓
𝟏
𝟕. 𝟑 𝟒
𝟓
8. 𝟕
𝟏𝟐
3. -𝟑
4. 𝟑𝟔
5. 𝟏𝟕
9. 0
10. -4
11. -3𝟖
𝟓
6.
-𝟐
𝟑
12. 100
CHANGING REPEATING DECIMALS TO A FRACTION
Work the following examples with the teacher.
Change each repeating decimal to its equivalent fraction or mixed number.
STEPS:
1. Let x equal your repeating decimal, now referred to as equation 1.
2. Multiply both sides of your equation by 10, 100, etc. depending on the number of digits in the repeating
pattern, now referred to as equation 2. Write this equation above equation 1.
3. Subtract equation 2 from equation 1.
4. Solve for x.
1. 0. 𝟒
2. 3. 𝟏𝟐
3. 20. 𝟓
INDEPENDENT PRACTICE:
4. 0. 𝟕
5. 2. 𝟎𝟓
6. 12. 𝟏𝟒
KEY:
1. Rational
2. Irrational
3. Rational, integer
4. Rational, integer, whole, counting
5. Irrational
6. Rational
7. Rational
8. Rational
9. Rational, integer, whole
10. Rational, integer
11. Rational
12. Rational, integer, whole, counting
10x = 4.4
100x = 312.12
x = 0.4
1. − − − − − −
9x = 4
x=
4
9
4. 7/9
10x = 205.5
x = 3.12
x = 20.5
2. − − − − − −
99x = 309
3. − − − − − −
9x = 185
x=
5. 2
309 103
4
=3
=
99
33
33
𝟓
𝟗𝟗
x=
6. 12
185
5
= 20
9
9
𝟏𝟒
𝟗𝟗