lesson
Preserve the decimal units
1 · Learn
Tenths, hundredths and thousandths are place-value units. Align decimal points for addition and subtraction so corresponding units share a column. Multiplying or dividing by powers of ten changes digit values; the decimal point is a separator, not a travelling digit.
When multiplying a decimal by a whole number, count the original units. Round at the requested final stage so repeated rounding does not distort the result.
A fraction can mean division: 3/8 means 3 divided by 8. Sharing 3.000 gives 0.375; multiplying 0.375 by 8 returns 3. For written decimal division, try 6.75 divided by 3. Six ones give two ones, seven tenths give two tenths with one tenth remaining, and that tenth plus five hundredths gives fifteen hundredths. Each group gets five hundredths, making 2.25. Keep decimal points aligned.
2 · Worked example
4.26 × 7 = 29.82 because 426 hundredths × 7 = 2,982 hundredths. Also 3.68 ÷ 100 = 0.0368.
3 · Your turn
Find 7.2 ÷ 8 and 3.045 × 6. Round 6.995 to two decimal places.
Check your answer
0.9; 18.27; 7.00.
4 · Apply your learning
Estimate each answer first and explain the zero placeholders in a decimal place-value grid.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish 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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