Final Answer:
-19 → Real, Rational, Integer
π → Real, Irrational
-2/3 → Real, Rational
42 → Real, Rational, Integer, Whole, Counting
√8 → Real, Irrational
0.582 → Real, Rational
0 → Real, Rational, Integer, Whole
2.51821... → Real, Irrational
√25 → Real, Rational, Integer, Whole, Counting
5. True
6. False (Example: 0.333... = 1/3 is rational)
7. True
8. True
9. True
10. True
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Explanation:
Let’s go one by one — don’t worry, it’s not as scary as it looks!
First, remember:
- “Real” means any number you can think of on a number line — so EVERY number here is Real.
- “Rational” = can be written as a fraction (like 1/2, -3, 0.75, etc.)
- “Irrational” = cannot be written as a fraction — like π or √2
- “Integer” = whole numbers, positive or negative, including zero (…-2, -1, 0, 1, 2…)
- “Whole” = 0, 1, 2, 3… (no negatives)
- “Counting” = 1, 2, 3… (starts at 1, no zero)
Now let’s check each number:
-
-19: It’s a negative whole number → Real, Rational, Integer
-
π: Never ends, never repeats → Real, Irrational
-
-2/3: It’s a fraction → Real, Rational
-
42: Positive whole number → Real, Rational, Integer, Whole, Counting
-
√8: √8 = about 2.828… and doesn’t repeat or end → Real, Irrational
-
0.582: Ends → can write as 582/1000 → Real, Rational
-
0: Zero is a whole number → Real, Rational, Integer, Whole
-
2.51821...: The “…” means it goes on forever without repeating → Real, Irrational
-
√25: √25 = 5 → which is a counting number → Real, Rational, Integer, Whole, Counting
Now the true/false part:
5. Square root of non-perfect square integer → always irrational?
→ Yes! Like √2, √3, √5 — they’re all irrational. So TRUE.
6. Never-ending decimal = always irrational?
→ No! Example: 0.333... = 1/3 → that’s rational! So FALSE.
7. Integers are always rational?
→ Yes! Any integer like -5, 0, 7 can be written as -5/1, 0/1, 7/1 → TRUE.
8. Square root of perfect square integer → always rational?
→ Yes! Like √9=3, √16=4 → both rational → TRUE.
9. All fractions are rational?
→ Yes! That’s what “rational” means — ratio of two integers → TRUE.
10. Whole numbers are always rational?
→ Yes! Whole numbers like 0, 1, 2 can be written as 0/1, 1/1, 2/1 → TRUE.
You got this! Just take it one step at a time.
Parent Tip: Review the logic above to help your child master the concept of number system worksheet.
