This worksheet builds fluency with place value, teaching students to write natural numbers in expanded notation using powers of 10. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Place value: each digit's value depends on its position — units, tens, hundreds, thousands, …
- 10⁰ = 1, 10¹ = 10, 10² = 100, 10³ = 1000 — each power of 10 has one more zero than the last.
- Expanded notation writes a number as the sum of each digit multiplied by its place value power of 10.
- E.g. 3758 = 3 × 10³ + 7 × 10² + 5 × 10¹ + 8 × 10⁰.
- A zero digit contributes nothing, so its term is left out of the expanded sum.
What your child will practise:
- Identifying the place value (power of 10) of each digit by counting positions from the right, starting at 10⁰.
- Writing a number in expanded notation: multiply each digit by its power of 10 and add the terms.
- Converting expanded notation back to a basic numeral by evaluating and adding each term.
- Skiping any place where the digit is 0 — it does not get a term in expanded notation.
- Recognising powers of 10 as a single digit times 10 to a power, e.g. 90 000 = 9 × 10⁴.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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