Multiplying and Dividing by 10, 100 and 1000
Multiplying and Dividing by 10, 100 and 1000 is the Year 4 topic covering how multiplying moves every digit one, two or three place-value columns to the left and dividing moves them the same number of columns to the right, understood as digits shifting rather than 'adding a zero'.
Before you start
Make sure you're comfortable with these topics first:
Method
- Picture a place value grid with thousands, hundreds, tens and ones columns (and more columns for bigger numbers).
- To multiply by 10, move every digit one column to the left; any empty column on the right is filled with a zero.
- To multiply by 100, move every digit two columns to the left (the same as multiplying by 10 twice); to multiply by 1000, move every digit three columns to the left.
- To divide by 10, 100 or 1000, move every digit the same number of columns to the right instead of left.
- Remember that 'adding a zero' only looks correct because whole numbers already end in the ones column; the real rule is that every digit's place value column changes.
- Check the answer is a sensible size: multiplying by 10, 100 or 1000 always makes a whole number bigger, and dividing by them always makes it smaller (as long as it divides exactly).
Worked example
Work out 34 x 100, and work out 8000 / 1000.
- For 34 x 100, move every digit two columns to the left: the 3 (tens) moves to the thousands column and the 4 (ones) moves to the hundreds column, with the two empty columns on the right filled with zeros.
- 34 x 100 = 3400.
- For 8000 / 1000, move every digit three columns to the right: the 8 moves from the thousands column to the ones column.
- 8000 / 1000 = 8.
Practice questions
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Q1Work out 27 x 10.Show answer
Answer: 270
Q2Work out 45 x 100.Show answer
Answer: 4500
Q3Work out 6 x 1000.Show answer
Answer: 6000
Q4Work out 5200 / 100.Show answer
Answer: 52
Q5Work out 90000 / 1000.Show answer
Answer: 90
Q6Work out 730 / 10.Show answer
Answer: 73
Q7A factory packs marbles into bags of 100. Deepak has 8 full bags. How many marbles does he have in total?Show answer
Answer: 800 marbles (8 x 100)
Q8Explain why 6 x 100 gives a different answer from 6 x 1000, even though both start with 6 x 1.Show answer
Answer: Multiplying by 100 moves the digit 6 two columns to the left (to the hundreds column), giving 600, while multiplying by 1000 moves it three columns to the left (to the thousands column), giving 6000; the more columns a digit moves, the bigger its new value becomes.
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Work out 82 x 1000.
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A school orders 100 identical boxes of paper. Each box weighs 67 kg. What is the total weight of all the boxes, in kilograms?
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A number is multiplied by 10, and then the result is multiplied by 100. The final answer is 68,000. What was the original number? Show your working.
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Free printable worksheet
Want more practice on paper? Download the multiplying and dividing by 10, 100 and 1000 worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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