Three ways to write one number
Every whole number can be written in three forms:
| Form | 4,205 written this way |
|---|---|
| Standard form | 4,205 |
| Expanded form | 4,000 + 200 + 5 |
| Word form | four thousand two hundred five |
They all mean the same amount. Each form is useful: standard form is short, expanded form shows place value, and word form is used on cheques and in speech.
The place value chart
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 4 | 2 | 0 | 5 |
| 4,000 | 200 | 0 | 5 |
The 0 in the tens place is a placeholder: there are no tens, but the zero keeps the other digits in the right places.
Expanded form step by step
- Write each digit times its place value.
- Skip any zeros (they add nothing).
- Join the values with plus signs.
Example: 63,708
- 6 is in the ten thousands place → 60,000
- 3 → 3,000
- 7 → 700
- 0 → skip
- 8 → 8
Expanded form: 60,000 + 3,000 + 700 + 8
Some classes also write expanded form with multiplication: (6 × 10,000) + (3 × 1,000) + (7 × 100) + (8 × 1).
Word form step by step
Big numbers are grouped in periods of three digits: ones, thousands, millions. Read each period like a small number, then say the period name.
Example: 305,412
- 305 thousand → "three hundred five thousand"
- 412 → "four hundred twelve"
Word form: three hundred five thousand four hundred twelve
Tips for word form:
- Use hyphens for numbers 21 to 99: forty-six, ninety-one.
- Don’t say "and" in whole numbers. In maths, "and" is saved for the decimal point.
- Commas in the word form are optional; many style guides leave them out.
Going back to standard form
Example: "seventy thousand sixty-four"
| Ten thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 7 | 0 | 0 | 6 | 4 |
Standard form: 70,064. Notice the two zeros needed as placeholders.
Worked examples
Example 1: Write 4,205 in expanded form.
4,000 + 200 + 5
Example 2: Write 9,000 + 40 + 2 in standard form.
There are no hundreds: 9,042.
Example 3: Write 2,617 in word form.
two thousand six hundred seventeen
Common mistakes
- Missing placeholder zeros: writing 9,000 + 40 + 2 as 942.
- Including zero terms in expanded form, like 4,000 + 200 + 0 + 5. Zero terms aren’t needed.
- Saying "and" in whole numbers: "two thousand and six" should be "two thousand six".
- Mixing up period names when reading large numbers.
Try it yourself
- Write 8,354 in expanded form.
- Write 50,000 + 600 + 3 in standard form.
- Write 12,045 in word form.
- Write "six hundred thousand twenty" in standard form.
Answers: 1) 8,000 + 300 + 50 + 4 2) 50,603 3) twelve thousand forty-five 4) 600,020
Quick recap
- Standard form uses digits; expanded form adds place values; word form uses words.
- Zeros are placeholders in standard form but are left out of expanded form.
- Read big numbers one period at a time.