Rational / Irrational Numbers
Name: ________________________________ Date: ________
Learning Target #1: I can identify rational and irrational numbers. (7.1.1.1)
Learning Target #2: I recognize that every rational number can be written as a terminating or
repeating decimal. (7.1.1.1)
Classify each number below as either rational or irrational. If you believe your number is rational, prove
your answer by writing it as a fraction. The first one is done for you.
Rational or Irrational?
1) 0.8
Rational
Fraction?
8
4
or 5
10
3
2) − 10
3) √40
4) √81
1
5) 2 3
6) 0.35
7) 0.33333 …
8)
−9
9)
3.4
10) √2
Directions: For each number shown, classify it as either rational or irrational, then tell whether or not it is
terminating or repeating.
(circle one)
(circle one)
11) -0.6
rational
or irrational
terminating, repeating, or neither
12)
rational
or irrational
terminating, repeating, or neither
rational
or irrational
terminating, repeating, or neither
rational
or irrational
terminating, repeating, or neither
rational
or irrational
terminating, repeating, or neither
13)
√100
2
5
14) −
2
3
15) 0.35217534 …
3
16) Which of the following is equivalent to 8 ?
a) 0.3
b) 0.45
c) 0.6
d) 0.375
17) Which of the following numbers is irrational?
a) 0.252525…
b) 0.875
c) 0.3754152…
d) -0.121212…
c) √64
d) -0.125374…
18) Which of the following numbers is rational?
a) √30
b) √42
18) Which of the following numbers is a terminating decimal?
7
a) √12
b) 8
c)
5
11
d) 0.81818181…
Mixed Review
Write each mixed number as an improper fraction.
3
2
19) 4 5
3
20) -23
21) 117
Compare the numbers below using >, <, or =.
22)
-14 ______ -12
23) |-5| _______ |-3|
24) -3.2 _______ -32
Place the numbers on the number line below.
25) 3.5
26) 3.7
3
27) 4.8
4
28) 3.05
5