This worksheet teaches students to multiply and divide decimals by 10, 100, 1000 and their multiples without a calculator, explaining the change using place value and checking with estimation. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Multiplying by 10 makes every digit worth 10 times more, so each digit moves one place to the left. Dividing by 10 moves each digit one place to the right.
- × 100 or ÷ 100 moves the digits 2 places; × 1000 or ÷ 1000 moves them 3 places.
- The decimal point doesn't move. The digits move to new place values around it.
- To multiply by a multiple of 10, split it up: × 30 is the same as × 3, then × 10.
- To divide by a multiple of 10, split it up: ÷ 20 is the same as ÷ 2, then ÷ 10.
What your child will practise:
- Multiplying and dividing decimals by 10, 100 and 1000.
- Explaining the change using place value (e.g. "5 tenths becomes 5 tens").
- Multiplying decimals by multiples of powers of 10 (20, 40, 300 …).
- Dividing decimals by multiples of powers of 10 (20, 30, 200, 500 …).
- Estimating using a multiple of 10 or 100 to check whether an answer is reasonable.
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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