Classify Numbers as Rational and Irrational Lesson Plan - 8th ... - Free Printable

To classify each number as rational or irrational, we need to remember:

- Rational numbers can be written as a fraction of two integers (like 1/2, -3, 0.75, or repeating decimals like 0.333...).
- Irrational numbers cannot be written as fractions — their decimal goes on forever without repeating (like π, √2, √10).

Let’s go one by one:

---

−2
This is an integer → can be written as −2/1 → rational

π
Pi is famous for being irrational — never ends, never repeats → irrational

√10
10 is not a perfect square → square root is not a whole number → irrational

√2
Also not a perfect square → irrational

0.̅3 (that’s 0.333...)
Repeating decimal → equals 1/3 → rational

−4.89786123
This looks like a terminating decimal (ends after 8 digits) → can be written as a fraction → rational

3½
Mixed number → equals 7/2 → rational

√25
25 is a perfect square → √25 = 5 → which is an integer → rational

π/2
Pi divided by 2 — still involves pi → still irrational → irrational

3π
Three times pi — still irrational → irrational

---

Now let’s list them clearly:

Rational:
−2, 0.̅3, −4.89786123, 3½, 25

Irrational:
π, 10, √2, π/2, 3π

Final Answer:
Rational: −2, 0.̅3, −4.89786123, 3½, √25
Irrational: π, √10, √2, π/2, 3π