Place Value Powers Worksheet

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📊 Part 1: Understanding Place Value and Powers of 10

1. What power of 10 does the digit 7 represent in the number 47,325?

10¹ (tens)

10² (hundreds)

10³ (thousands)

10⁴ (ten thousands)

2. Which of the following correctly shows 5,642 in expanded form using powers of 10?

5×10¹ + 6×10² + 4×10³ + 2×10⁴

5×10³ + 6×10² + 4×10¹ + 2×10⁰

5×10⁴ + 6×10³ + 4×10² + 2×10¹

3. The decimal 0.37 can be written as:

3×10¹ + 7×10⁰

3×10⁰ + 7×10⁻¹

3×10⁻¹ + 7×10⁻²

4. Fill in the blanks with the correct powers of 10:

In the number 892.45:

• The digit 8 is in the _______ place, which represents 10___

• The digit 9 is in the _______ place, which represents 10___

• The digit 4 is in the _______ place, which represents 10___

🔄 Part 2: Multiplying and Dividing by Powers of 10

5. Complete the following calculations:

a) 234 × 10 = _______

b) 67.8 × 10 = _______

c) 1,450 ÷ 10 = _______

d) 8.9 ÷ 10 = _______

6. When you multiply a number by 10, what happens to each digit's position?

7. A shop sells chocolate bars for $3.50 each. If they increase the price by multiplying by 10, what would be the new price? Explain why this might not be realistic!

✏️ Part 3: Problem Solving with Place Value

8. Write these numbers in expanded form using powers of 10:

a) 7,304 = ________________________________

b) 52.16 = ________________________________

c) 90,087 = _______________________________

9. A scientist measures the distance between two cities as 2.47 × 10² kilometres. Write this distance in standard form.

Distance = _______ kilometres

10. Real-world problem: The population of Auckland is approximately 1.7 × 10⁶ people. If the population increased by a factor of 10, what would the new population be? Write your answer in both power of 10 notation and standard form.