Lesson 4 of 10 · Grades 3 to 4
Multiplying by 10 and 100
Multiplying by 10 is the tidiest multiplication there is. Nothing about the digits changes; only their place value changes. Multiplying by 100 does the same thing twice over. Once you see the pattern, you can multiply big round numbers in your head.
A place value pattern
Multiplying by 10 changes where each digit lives, not what it is. Take the number 24. The digit 2 sits in the tens place and means 20. The digit 4 sits in the ones place and means 4. Now multiply by 10. The digit 2 moves to the hundreds place and means 200. The digit 4 moves to the tens place and means 40. The answer is 240, and not a single digit changed shape.
Multiplying by 100 does the same thing twice. Every digit moves two places to the left: 24 becomes 2400. The 2 now means 2000 and the 4 now means 400. Moving left, the digits become worth ten times more each time.
Where do the zeros come from?
The zeros are place holders. When 24 is multiplied by 10, the digit 4 steps out of the ones place, and nothing is left behind, so a zero takes its place. Multiplying by 100 leaves two empty places, so two zeros stand in. This is why multiplying a whole number by 10 adds one zero and multiplying by 100 adds two.
Be careful: the rule about adding zeros only works for whole numbers written in the usual way. It works because our number system is built on groups of ten. It is not a magic trick; it is place value doing its job.
Tens as factors
Once you can multiply by 10, you can multiply by 20, 30, 70 and the rest. Think of 20 as 2 × 10. To work out 6 × 20, multiply by 2 first and by 10 second: 6 × 2 = 12, then 12 × 10 = 120. To work out 9 × 70, do 9 × 7 = 63, then multiply by 10 for 630.
The order you do the two steps in does not matter. You can multiply by 10 first and by 2 second, and you still get the same answer. Splitting a round number into a small factor and a power of ten turns a big-looking multiplication into a small one.
Watch out for this
Multiplying by 10 is not the same as adding 10. 25 × 10 = 250, while 25 + 10 = 35. Also check the number of zeros: 7 × 100 = 700, with two zeros, not one. Say the place values to yourself as a check: 7 ones becomes 7 hundreds.
Worked example
A library shelf holds 100 books. How many books are on 34 shelves?
Step 1: every shelf holds the same 100 books, so multiply 34 × 100.
Step 2: multiplying by 100 moves each digit two places to the left: 34 becomes 3400.
Step 3: check with the pattern. Multiplying by 10 gives 340, and multiplying that by 10 again gives 3400.
Answer: 3400 books.
Remember
- Multiplying by 10 moves every digit one place to the left.
- Multiplying by 100 moves every digit two places to the left.
- A whole number times 10 ends in one zero; times 100 ends in two.
- For 20, 30 and 70, multiply by the small factor, then by 10.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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What is 7 × 10?
Show answer
70. The 7 moves to the tens place and a zero fills the ones place.
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What is 7 × 100?
Show answer
700. The 7 moves to the hundreds place.
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What is 36 × 10?
Show answer
360.
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What is 36 × 100?
Show answer
3600.
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A box holds 10 pencils. How many pencils are in 25 boxes?
Show answer
250 pencils. 25 × 10 = 250.
Puzzle · Pattern cards
Puzzle time
The cards show a pattern for multiplying 24. What number belongs in the last card?
Show a hint
Multiplying by 100 moves every digit two places to the left, so 24 gains two zeros.
Show the answer
Answer: 2400. 24 × 100 = 2400. Each card multiplies by ten more than the one above, so the last card has two more zeros than 24. The answer 240 is only ten times 24, and 2040 keeps the digits in the wrong places.