Mrs.D Math · 8th Grade

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Ordering Real Numbers · Number System
🔢 Real Numbers
🌀 Irrational Numbers
➗ Rational Numbers
⚖️ √20 > 4.4
📊 π, 22/7, 3.14…
🧮 √2 ≈ 1.414
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📚 Ordering Real Numbers

The Real Number Family

Rational numbers can be written as a fraction — their decimals end or repeat. Irrational numbers never end and never repeat.

➗
Rational: fractions, terminating decimals, repeating decimals, and perfect square roots
½   3.75   0.333…   √25 = 5
🌀
Irrational: non-perfect square roots and π — the decimal goes on forever without a pattern
√20 ≈ 4.4721…   π ≈ 3.14159…

How to Compare & Order Them

1
Convert every number to a decimal. Use your calculator for square roots and fractions.
√20 ≈ 4.472    9/2 = 4.5    4.4 = 4.444…
2
Line up the decimals and compare place by place — write two or three decimal places for close numbers.
3
Watch the negatives! On the left side of zero, the number that looks bigger is actually smaller.
−5.5 < −5.48

How to Play

⚖️
Compare — Pick the number with the greatest or least value from 4 choices.
📊
Order It — Drag (or tap) the number tiles into the slots in the correct order, then hit CHECK.
🔀
Mixed — Both types together for the ultimate challenge!
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