Place-Value Powers of Ten

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Part 1: Place-Value Relationships

Use powers of ten to explain how the value of a digit changes when it moves from one place to another.

1. What is the value of the digit 7 in 7,000? Write your answer using a power of ten.

2. In 45,000 and 4,500, the digit 5 moves one place to the left. How does its value change?

It becomes 10 times greater.

It becomes 10 times less.

It stays the same.

3. Complete the equation: 8 × 10³ = _________

4. In the number 6,482,000, what is the value of the digit 6? What would its value be if it moved one place to the right?

For each problem, follow the highlighted digit as it moves left or right. Record its new value and describe the change.

5. Start with 3 in 3,000. Move the digit one place to the right. New value: _________. Change: ______________________________

6. Start with 4 in 40,000. Move the digit two places to the right. New value: _________. Change: ______________________________

7. Complete the chart for the highlighted digit in 5,000,000.

Starting value: 5,000,000 = ____________________

Move one place right: 500,000 = ____________________

Move two places right: 50,000 = ____________________

Move one place left: 50,000,000 = ____________________

8. The highlighted digit is 9. Complete the sequence as the digit moves left.

9 → 90 → __________ → __________

Write the power-of-ten relationship for each move: __________________________________________

9. Write a rule explaining why moving a digit one place to the left makes its value 10 times greater.

10. Write a rule explaining why moving a digit one place to the right makes its value 10 times less. Include a power of ten in your explanation.