I.2 Multiply multiples of 10, 100, and 1,000 by 1-digit numbers
Understanding place value up to thousands
Place value is the value of a digit based on its position in a number. In the number 4,382, the digit 4 is in the thousands place, so it represents 4,000. The digit 3 is in the hundreds place and represents 300. The digit 8 is in the tens place and represents 80. The digit 2 is in the ones place and represents 2. When we multiply by multiples of 10, 100, or 1,000, we are really multiplying the digits and then using place value to determine the size of the final product.
- In 7,000, the digit 7 is in the thousands place, meaning 7 thousands.
- In 900, the digit 9 is in the hundreds place, meaning 9 hundreds.
- In 60, the digit 6 is in the tens place, meaning 6 tens.
Understanding place value helps us see that 5,000 is actually 5 × 1,000. This idea is the key to multiplying larger numbers quickly.
What are multiples of 10, 100, and 1,000?
Multiples of a number are the result of multiplying that number by any whole number. A multiple of 10 is any number that ends with a zero, such as 20, 50, or 170. A multiple of 100 ends with two zeros, like 400 or 1,300. A multiple of 1,000 ends with three zeros, like 7,000 or 9,000.
- 10, 20, 30, 40, 50, 60, 70, 80, and 90 are multiples of 10.
- 100, 200, 300, 400, 500, 600, 700, 800, and 900 are multiples of 100.
- 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, and 9,000 are multiples of 1,000.
When a number is a multiple of 10, 100, or 1,000, it is built from a basic fact multiplied by a power of ten. For example, 7,000 is 7 × 1,000.
The basic rule: multiply the basic fact, then attach the zeros
When you multiply a multiple of 10, 100, or 1,000 by a 1-digit number, follow these two simple steps. First, ignore the zeros and multiply the basic fact. Second, count the total number of zeros in both factors and attach that many zeros to the product from step one.
- For 30 × 4, think 3 × 4 = 12, then attach one zero: 120.
- For 500 × 6, think 5 × 6 = 30, then attach two zeros: 3,000.
- For 2,000 × 3, think 2 × 3 = 6, then attach three zeros: 6,000.
Always count the zeros carefully. 6,000 has three zeros because 2,000 has three zeros and 3 has zero zeros. The total zeros attached is three.
Multiplying multiples of 10 by 1-digit numbers
A multiple of 10 is a number like 40, 70, or 90. To multiply it by a 1-digit number, multiply the non-zero digit by the 1-digit number. Then, place one zero at the end of the result.
- 40 × 5 = 20040× 5200
Because 4 × 5 = 20, and then we add one zero. - 70 × 8 = 56070× 8560
Because 7 × 8 = 56, and then we add one zero. - 90 × 3 = 27090× 3270
Because 9 × 3 = 27, and then we add one zero.
Check your work: 40 × 5 means 40 + 40 + 40 + 40 + 40 = 200. The shortcut works every time.
Multiplying multiples of 100 by 1-digit numbers
A multiple of 100 ends in two zeros, such as 200, 500, or 800. Multiply the non-zero digit by the 1-digit number. Then, place two zeros at the end of that product.
- 200 × 4 = 800200× 4800
Because 2 × 4 = 8, and then we add two zeros. - 300 × 3 = 900300× 3900
Because 3 × 3 = 9, and then we add two zeros. - 600 × 7 = 4,200600× 74,200
Because 6 × 7 = 42, and then we add two zeros.
When you attach two zeros, you are multiplying by 100. For 600 × 7, you are really doing 6 × 100 × 7 = (6 × 7) × 100 = 42 × 100 = 4,200.
Multiplying multiples of 1,000 by 1-digit numbers
A multiple of 1,000 ends in three zeros, like 4,000, 7,000, or 9,000. To multiply, multiply the non-zero digit by the 1-digit number. Then, place three zeros at the end of that product.
- 4,000 × 2 = 8,0004,000× 28,000
Because 4 × 2 = 8, and then we add three zeros. - 5,000 × 5 = 25,0005,000× 525,000
Because 5 × 5 = 25, and then we add three zeros. - 7,000 × 9 = 63,0007,000× 963,000
Because 7 × 9 = 63, and then we add three zeros.
Be careful with commas. 25,000 has a comma after the thousands place, but it still has three zeros at the end.
Working with numbers that have internal zeros
Sometimes the basic fact already ends in a zero. For example, 5 × 6 = 30. When we attach zeros to a product that ends in zero, we need to combine them correctly. The total zeros in the final answer is the sum of zeros from both factors plus any zeros from the basic fact.
- 50 × 6 = 30050× 6300
5 × 6 = 30, and 50 has one zero. 30 already has one zero, so we have two zeros total: 300. - 500 × 8 = 4,000500× 84,000
5 × 8 = 40, and 500 has two zeros. 40 has one zero, so we have three zeros total: 4,000. - 2,000 × 5 = 10,0002,000× 510,000
2 × 5 = 10, and 2,000 has three zeros. 10 has one zero, so we have four zeros total: 10,000.
Always count the zeros in the basic fact product and add them to the zeros from the multiple. 50 × 6 is 300, not 30 with one zero attached (which would be 300 anyway), but this method ensures accuracy for larger numbers.
Using place value to explain the pattern
When we multiply 300 by 4, we can think of 300 as 3 hundreds. So, 3 hundreds × 4 = 12 hundreds. 12 hundreds is the same as 1,200.
- 70 × 8: 7 tens × 8 = 56 tens = 560.
- 600 × 3: 6 hundreds × 3 = 18 hundreds = 1,800.
- 9,000 × 2: 9 thousands × 2 = 18 thousands = 18,000.
Thinking in terms of place value helps you understand why the shortcut works. 18 thousands is 18,000 because one thousand is 1,000, and 18 × 1,000 = 18,000.
Real-world application of multiplying large numbers
Knowing how to multiply multiples of 10, 100, and 1,000 helps in everyday situations. If you buy 4 books that each cost 200, you can quickly find the total cost. If a school has 3,000 students and each student donates 2, you can find the total donation amount.
- A pencil costs 30¢. How much do 6 pencils cost? 30 × 6 = 180¢, which is $1.80.
- A theater has 800 seats. If 5 shows are sold out, how many tickets were sold? 800 × 5 = 4,000 tickets.
- A factory produces 2,000 toys each day. How many toys are produced in 8 days? 2,000 × 8 = 16,000 toys.
Always ask yourself: Does my answer make sense? 800 seats times 5 shows should be around 4,000, not 400 or 40,000. Estimating helps you check your work.
Common mistakes to avoid
Students sometimes attach the wrong number of zeros or forget to multiply the basic fact correctly. Another common mistake is to multiply the zeros themselves instead of the non-zero digits.
- Incorrect: 40 × 5 = 20 (forgot to attach the zero). Correct: 40 × 5 = 200.
- Incorrect: 300 × 3 = 90 (attached only one zero). Correct: 300 × 3 = 900.
- Incorrect: 6,000 × 4 = 240,000 (attaching four zeros, but 6,000 has three zeros). The correct answer is 24,000.
Double-check the number of zeros. 6,000 has three zeros. 4 has zero zeros. Total zeros = 3. So 6 × 4 = 24, then attach three zeros: 24,000. Not 240,000.
Practice with mixed examples
Here are more examples that mix multiples of 10, 100, and 1,000. See if you can spot the pattern.
- 90 × 3 = 27090× 3270
- 700 × 6 = 4,200700× 64,200
- 8,000 × 7 = 56,0008,000× 756,000
- 50 × 8 = 40050× 8400
- 200 × 9 = 1,800200× 91,800
- 3,000 × 4 = 12,0003,000× 412,000
Notice that 1,800 has a comma, and 12,000 has a comma. Commas help us read large numbers, but they do not change the zeros count. 12,000 still has three zeros at the end.
Extending the pattern to larger numbers
The same pattern works for numbers like 10,000 (ten thousands), 100,000 (hundred thousands), and 1,000,000 (millions). For now, we focus on thousands, but knowing the rule helps you solve any similar problem.
- 10,000 × 3 = 30,000 (1 × 3 = 3, attach four zeros).
- 200,000 × 4 = 800,000 (2 × 4 = 8, attach five zeros).
- 3,000,000 × 2 = 6,000,000 (3 × 2 = 6, attach six zeros).
The pattern never changes: multiply the non-zero digits, then count and attach all the zeros from both factors.
Summary of key ideas
To multiply a multiple of 10, 100, or 1,000 by a 1-digit number, first find the product of the non-zero digits. Then, count the total number of zeros in the multiple and attach them to the product.
- 30 × 4 = 120 (3 × 4 = 12, plus one zero)
- 500 × 6 = 3,000 (5 × 6 = 30, plus two zeros = 3,000)
- 4,000 × 7 = 28,000 (4 × 7 = 28, plus three zeros = 28,000)
If the basic fact product already ends in zero, you still add the zeros from the multiple. For example, 50 × 6 = 300 because 5 × 6 = 30, and 50 has one zero, so 30 with one zero attached is 300.
Common Core alignment: CCSS.MATH.CONTENT.4.NBT.B.5 – Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.B.5. It focuses on the foundational skill of multiplying multiples of 10, 100, and 1,000 by 1-digit numbers, which supports the development of fluency in multiplying larger numbers. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework.