lesson
Every digit changes value
1 · Learn
Multiplying by ten makes each digit worth ten times as much. Dividing by ten makes each worth one tenth as much. The decimal point separates ones and tenths; it is not a movable digit.
For 3.45 × 100, the digits represent 345. For 7 ÷ 1,000, they represent 0.007. Adding or removing zeros is not a reliable general method.
2 · Worked example
I work out 0.62 × 1,000 = 620 using place values, then divide by 1,000 to check the original value returns.
3 · Your turn
Find 4.08 × 10, 32.5 ÷ 100 and 0.9 × 1,000.
Check your answer
40.8; 0.325; 900.
4 · Apply your learning
Track each digit on a place-value chart for multiplication and division by 10, 100 and 1,000.
Adult guidance and safety
Model the calculation or measurement before relying on a procedure. Explain estimates, units and checks. Use a ruler/protractor and suitable diagrams where needed; text examples alone do not establish practical skill or fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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