What does multiplying by 10 or 100 mean?
Multiplying by 10 or 100 means you take a number and make it 10 times larger or 100 times larger. It is a shortcut for repeated addition. When we multiply a whole number by 10, each digit in the number moves one place to the left. When we multiply by 100, each digit moves two places to the left. This is called a place‑value shift.
- 7 × 10 = 70 (7 groups of 10)
- 7 × 100 = 700 (7 groups of 100)
- 15 × 10 = 150
- 15 × 100 = 1,500
Understanding place value is the key. When you multiply by 10, the number becomes 10 times greater. When you multiply by 100, it becomes 100 times greater.
Strategy 1: Use the place value chart
A place value chart helps us see how digits shift to the left when we multiply by 10 or 100. Each time we multiply by 10, we move one column to the left. Zeros hold the empty places.
- Think of 34 as 3 tens and 4 ones.
- Multiply by 10: each ten becomes a hundred, and each one becomes a ten.
- So 3 tens become 3 hundreds, and 4 ones become 4 tens.
- The number is now 3 hundreds, 4 tens, and 0 ones = 340.
- Multiply by 100 means we shift two places left.
- 3 tens become 3 thousands; 4 ones become 4 hundreds.
- So we have 3 thousands, 4 hundreds, 0 tens, 0 ones = 3,400.
Always line up your digits. Moving left increases the value of each digit. Drawing a simple place‑value chart on paper can prevent mistakes.
Strategy 2: Use the "attach zeros" shortcut
Because of place value, there is a fast rule: to multiply a whole number by 10, attach one zero to the right end. To multiply by 100, attach two zeros. This works because you are increasing the place value of every digit.
- 82 × 10 = 820 (attach one zero)
- 82 × 100 = 8,200 (attach two zeros)
- 450 × 10 = 4,500 (attach one zero; careful: 450 already has one zero)
- 7,000 × 100 = 700,000 (attach two zeros to 7,000 → 700,000)
This shortcut works for whole numbers. If you have a decimal, the digits shift, but you do not simply "add zeros." For fourth grade, we focus on whole numbers.
Strategy 3: Use repeated addition
Multiplication is repeated addition. So 23 × 10 means 23 added together 10 times. This strategy helps us understand why the product makes sense, even if it is slower.
- 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 80
- You can count by 8 ten times: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
- 12 added 100 times is too long to write, but you can think: 12 × 10 = 120, and then 120 × 10 = 1,200 (since 100 = 10 × 10). Another way: 12 × 100 = 12 × 10 × 10 = 120 × 10 = 1,200.
Repeated addition is useful for small numbers, but for larger numbers, use the place‑value shift or the shortcut.
Strategy 4: Use basic facts and then multiply by 10 or 100
Break the problem into two steps: first multiply the non‑zero digits (the basic fact), then apply the place‑value shift. This is sometimes called the associative property.
- Think of 90 as 9 × 10.
- First, 6 × 9 = 54.
- Then multiply by 10: 54 × 10 = 540.
- So 6 × 90 = 540.
- 400 = 4 × 100.
- First, 7 × 4 = 28.
- Then multiply by 100: 28 × 100 = 2,800.
- So 7 × 400 = 2,800.
This strategy works for any number that is a multiple of 10 or 100. It builds on mental math skills.
Multiplying larger numbers by 10 or 100
When numbers have more digits, the same rules apply. Each digit shifts left, and we add zeros as placeholders. Commas help us read large numbers.
- 3,425 × 10 = 34,250 (each digit moves left, one zero added)
- 3,425 × 100 = 342,500 (each digit moves left two places, two zeros added)
- 1,000 × 100 = 100,000 (1,000 has three zeros; ×100 adds two more, total 5 zeros → 100,000)
- 12,506 × 10 = 125,060 (careful: the zero in the tens place shifts and a new zero is added)
Always count the zeros carefully. When you multiply by 10, you add exactly one zero. When you multiply by 100, you add exactly two zeros. But if the original number already ends with zeros, the total number of zeros at the end will be the original zeros plus the added ones.
Real-world word problems
Applying multiplication by 10 or 100 to real situations helps you understand when to use it.
A bakery makes 245 muffins each day. How many muffins do they make in 10 days?
Solution: 245 × 10 = 2,450 muffins.
A library has 3,870 books. Each book has about 100 pages. About how many pages in total?
Solution: 3,870 × 100 = 387,000 pages.
A school district orders 52 boxes of notebooks. Each box holds 100 notebooks. How many notebooks is that?
Solution: 52 × 100 = 5,200 notebooks.
Read the problem carefully. Does it say "each day for 10 days"? That is a clue to multiply by 10. If it says "each box holds 100," multiply by 100.
Mental math and patterns
Practicing multiplication by 10 and 100 builds mental math fluency. Look for patterns: 6 × 10 = 60, 60 × 10 = 600, 600 × 10 = 6,000. Each time you multiply by 10, you add a zero.
- 14 × 10 = 140
- 14 × 100 = 1,400
- 140 × 10 = 1,400 (same as 14 × 100)
- 1,400 × 10 = 14,000
- 1,400 × 100 = 140,000
Notice that 14 × 100 = 1,400 and 140 × 10 = 1,400. Multiplying by 100 is the same as multiplying by 10 twice.
Common mistakes to avoid
Even fourth graders can make errors. Watch out for these common pitfalls.
- Wrong: 56 × 10 = 5,600? No, that would be 56 × 100.
- Correct: 56 × 10 = 560
- Wrong: 305 × 10 = 3,005.
- Correct: 305 × 10 = 3,050.
- Incorrect: 1234 × 100 = 123400 (hard to read).
- Correct: 1,234 × 100 = 123,400.
Always check your work by thinking about place value. If you multiply by 100, the number should be much larger.
Review: all strategies in one place
Here is a quick summary of the ways to multiply by 10 or 100.
- Place value shift: Move digits left, fill with zeros.
- Attach zeros: Add one zero for ×10, two zeros for ×100.
- Repeated addition: Add the number over and over.
- Basic facts first: Multiply the non‑zero part, then apply 10 or 100.
- Mental math patterns: Use known facts to build fluency.
No matter which strategy you use, the result is the same. Choose the strategy that makes the most sense to you.
Challenge: multiply by multiples of 10 and 100
Sometimes you need to multiply by numbers like 30 or 200. You can break them into 3 × 10 or 2 × 100 and use two steps.
- 30 = 3 × 10.
- First, 45 × 3 = 135.
- Then, 135 × 10 = 1,350.
- So 45 × 30 = 1,350.
- 400 = 4 × 100.
- First, 62 × 4 = 248.
- Then, 248 × 100 = 24,800.
- So 62 × 400 = 24,800.
This is an extension of the "basic facts first" strategy. It works for any number that ends with zero.
Word problems with larger numbers
Real life often involves large numbers. Use commas and check your zeros.
A warehouse has 1,250 boxes. Each box weighs 10 pounds. What is the total weight?
Solution: 1,250 × 10 = 12,500 pounds.
A state park had 42,675 visitors last year. This year, the number of visitors was 10 times of the last year. How many visitors this year?
Solution: 42,675 × 10 = 426,750 visitors.
A company prints 9,500 flyers every day for 100 days. How many flyers in total?
Solution: 9,500 × 100 = 950,000 flyers.
When multiplying numbers that already end with zeros, count all the zeros at the end. 9,500 has two zeros; ×100 adds two zeros; total four zeros.
Common Core alignment:
CCSS.MATH.CONTENT.4.NBT.A.1 – Recognize that in a multi‑digit whole number, a digit in one place represents ten times what it represents in the place to its right.
CCSS.MATH.CONTENT.4.NBT.A.3 – Use place value understanding to multiply whole numbers by 10 or 100.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.A.1 and 4.NBT.A.3. All content is 100% free, use it for whole‑class instruction, independent study, practice, or homework. The strategies presented build conceptual understanding of place value and multiplication by 10 and 100.