Place Value Patterns

Grade 3 · mathematics · 101 practice problems · read aloud

🔊 Listen to this explanation

Place Value Patterns

🧠 What is it and Why is it Useful?

Place value patterns help us understand how numbers grow or shrink when we multiply or divide by 10, 100, or 1,000. It's like a number shortcut! Instead of doing long calculations, we can just move the digits. This is useful because it makes working with big numbers much faster and easier.

📝 How to Solve Problems: A Step-by-Step Guide

  1. Identify the Operation: Are you multiplying or dividing by 10, 100, or 1,000?
  2. Find the Digits: Look at the number you are starting with.
  3. Move the Digits:
    • Multiply: Move digits to the LEFT. Each zero in 10, 100, etc., tells you how many places to move.
    • Divide: Move digits to the RIGHT. Each zero in 10, 100, etc., tells you how many places to move.
  4. Check Your Work: Make sure your new number makes sense!

🔢 Visual Examples

Example 1: Multiplying by 100

What is 45 × 100?

Think: 100 has two zeros, so we move the digits two places to the left.

45 → 4 5 . → 4, 5 0 0

Answer: 4,500

Example 2: Dividing by 10

What is 3,200 ÷ 10?

Think: 10 has one zero, so we move the digits one place to the right.

3,200 → 3 2 0 0 . → 3 2 0 . 0 or just 320

Answer: 320

⚠️ Common Mistakes

Moving Digits the Wrong Way: Remember, multiplying makes numbers bigger, so digits move left. Dividing makes numbers smaller, so digits move right.

Forgetting Zeroes as Placeholders: When you move a digit, you must fill the empty space with a zero. For example, 7 × 10 is 70, not 7.

💡 Tips & Tricks

The Decimal Point Dance: Imagine a decimal point at the end of a whole number. When you multiply, the decimal point moves right. When you divide, it moves left. (The digits appear to move the opposite way!).

Zero Counter: Count the zeros in the number you are multiplying or dividing by (like 10, 100). That's how many places the digits move!

🎯 How to Practice

  • Flashcards: Make cards with problems like "60 × 10" or "8,400 ÷ 100" and quiz yourself.
  • Number Roll: Write a number on a whiteboard. Have a partner say "× 100" or "÷ 10" and you solve it by moving the digits.
  • Real-World Problems: "If one box holds 10 pencils, how many pencils are in 30 boxes?"

Practice problems

6 of the 101, worked through step by step — try them before opening the answer.

1 324 × 6 = ?

Hint: Multiply the ones place first, then the tens place, and finally the hundreds place, remembering to carry over when needed.

Show the answer

Answer: 1944

  1. Break down 324 by place values. 324 = 300 + 20 + 4
  2. Multiply each part by 6. First, 300 × 6 = 1800 Second, 20 × 6 = 120 Third, 4 × 6 = 24
  3. Add the results together. 1800 + 120 = 1920 1920 + 24 = 1944
  4. Check the multiplication using the standard algorithm for confirmation: Write it vertically: 324 × 6 First, multiply 6 × 4 = 24 → write down 4, carry over 2. Next, multiply 6 × 2 = 12, plus the carried 2 = 14 → write down 4, carry over 1. Finally, multiply 6 × 3 = 18, plus the carried 1 = 19 → write down 19. So the result is 1944. ANSWER: 1944

Let's multiply 324 × 6 step by step.

2 85 × 10 = ?

Hint: Think about what happens to each digit when you multiply a number by 10. The digits shift one place to the left, and a zero is added at the end.

Show the answer

Answer: 850

  1. Write 85 as 8 tens and 5 ones.
  2. Multiply each part by 10: 8 tens × 10 = 8 hundreds (800), and 5 ones × 10 = 5 tens (50).
  3. Add the results: 800 + 50 = 850.
  4. Notice the pattern: 85 × 10 = 850. The digits 8 and 5 moved one place to the left, and a 0 was added at the end.

The answer is 850.

3 36 × 10 = ?

Hint: Think about what happens to each digit when you multiply by 10. The digits shift one place to the left.

Show the answer

Answer: 360

  1. Write 36 as 3 tens and 6 ones.
  2. Multiply each part by 10: 3 tens × 10 = 3 hundreds (300), 6 ones × 10 = 6 tens (60).
  3. Add the results: 300 + 60 = 360. So, 36 × 10 = 360.

4 648 ÷ 10 = ?

Hint: Think about what happens to each digit when you divide by 10. The digits shift one place to the right.

Show the answer

Answer: 64.8

  1. Write 648 as 648.0 to help see the decimal point.
  2. When dividing by 10, each digit moves one place to the right.
  3. The hundreds digit 6 moves to the tens place, the tens digit 4 moves to the ones place, and the ones digit 8 moves to the tenths place.
  4. So 648 ÷ 10 = 64.8.

The answer is 64.8.

5 361 × 10 = ?

Hint: Think about what happens to each digit when you multiply by 10. The digits shift one place to the left, and a zero is added at the end.

Show the answer

Answer: 3610

  1. Write 361 in expanded form: 300 + 60 + 1.
  2. Multiply each part by 10: 300 × 10 = 3000, 60 × 10 = 600, 1 × 10 = 10.
  3. Add the results: 3000 + 600 + 10 = 3610.
  4. Notice the pattern: the digits 3, 6, 1 all shift one place to the left, and a 0 is added in the ones place.

The answer is 3610.

6 624 ÷ 10 = ?

Hint: Think about what happens to each digit when you divide by 10. The digits shift one place to the right.

Show the answer

Answer: 62.4

  1. Write 624 as 600 + 20 + 4.
  2. Divide each part by 10: 600 ÷ 10 = 60, 20 ÷ 10 = 2, 4 ÷ 10 = 0.4.
  3. Add the results: 60 + 2 + 0.4 = 62.4.
  4. Using place value: the 6 moves from the hundreds place to the tens place (60), the 2 moves from the tens place to the ones place (2), and the 4 moves from the ones place to the tenths place (0.4).

The answer is 62.4.

Practise this topic — 10 free problems, no signup →