What are whole numbers?

Whole numbers are the numbers 0, 1, 2, 3, 4, 5, ... — that is, zero and all the positive integers. They do not include negative numbers, fractions or decimals. Whole numbers are used for counting whole objects.

Set notation: {0, 1, 2, 3, ...}

Examples (Kenyan context)

• Number of pupils in a class: 45 (whole number)
• Shillings in a coin problem: 50 KSh (whole number value)
• Number of trees on a farm: 120 (whole number)
• 0 cows on a farm (zero is a whole number)

Number line (visual)

All marked points are whole numbers:

Note: All whole numbers lie on and to the right of 0 on the number line (no negatives).

Place value (quick)

Example: 4 372

Value = 4 × 1000 + 3 × 100 + 7 × 10 + 2 × 1 = 4 372

Properties of whole numbers

• Closure: Addition and multiplication of whole numbers give whole numbers. (e.g. 3 + 5 = 8, 4 × 2 = 8)
• Commutative: a + b = b + a ; a × b = b × a
• Associative: (a + b) + c = a + (b + c) ; (a × b) × c = a × (b × c)
• Identity elements: 0 is additive identity (a + 0 = a). 1 is multiplicative identity (a × 1 = a).
• Subtraction and division: Not always whole. Example: 5 − 8 = −3 (not whole), 7 ÷ 2 = 3.5 (not whole).

Even, odd, prime and composite (short)

Even: divisible by 2 (0, 2, 4, 6, ...). Odd: not divisible by 2 (1, 3, 5, ...).

Prime: a whole number greater than 1 with exactly two factors (e.g. 2, 3, 5, 7).

Composite: a whole number greater than 1 that has more than two factors (e.g. 4, 6, 8).

Rounding whole numbers

To round to the nearest ten: look at units digit.

Example: Round 426 to the nearest ten. Units = 6 → round up → 430.

Example: Round 213 to the nearest hundred. Tens digit = 1 → round down → 200.

Worked examples

1. Problem: Add 347 + 506.
   347 + 506 = (300+40+7) + (500+0+6) = 800 + 40 + 13 = 800 + 53 = 853.
2. Problem: Is 0 a whole number? Give an example.
   Yes. Example: 0 cows on a field — we can count zero cows.
3. Problem: Which is larger: 2 009 or 1 999?
   2 009 is larger because the thousands digit (2) > (1).

Try these (short practice)

1. Write five whole numbers between 10 and 20.
2. Round 1 347 to the nearest hundred.
3. Find 84 ÷ 7. Is the answer a whole number?
4. Which of these are whole numbers: −2, 0, 3.5, 100?
5. Is 1 a prime number? Explain briefly.

Why whole numbers matter

Whole numbers are used in everyday life: counting people, money, goods, measuring whole items (pupils, books, trees). They build the base for other topics like fractions, integers and algebra.