DIRECTIONS: Write R if the number can be written as a fraction of two whole numbers, I if it cannot.
Rational: one whole number over another. Its decimal stops
or repeats (0.25, 0.333…). Irrational: the decimal never stops and never repeats, like
√2 = 1.41421356…
Part A — R or I?
1.
0.101001000100001… (one more zero each time)
2.
√7
3.
√121
4.
√9
5.
0.35
6.
π
7.
√2
8.
4⁄3
9.
22⁄7
10.
√18
11.
−13
12.
0.333333…
When the Fractions Run Out — continued
Grade 8 · Number · Page 2 of 2
√16 = 4, rational. √17 = 4.1231056…, irrational.
Look under the root sign: is it a perfect square?
Part B — Rational or irrational? If it is rational, write what it equals.
13.
√36=
14.
√12=
15.
√3=
16.
√10=
17.
√13=
18.
√49=
Part C — Explain it.
Ella says √25 must be irrational, “because it has a square root sign on it.” Is she right? What is √25, and what should she have looked at instead?
22⁄7 is often used in place of π. Is 22⁄7 rational or irrational? Is π? And are the two numbers equal — how would you check?
A calculator shows √2 = 1.414213562. Square that number by hand. Does it come out as exactly 2? What does that tell you about what the screen was showing you?