Decimals and Powers of Ten

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📊 Part 1: Moving the Decimal Point

1. When multiplying by 10, the decimal point moves _______ place(s) to the _______.

2. When dividing by 100, the decimal point moves _______ place(s) to the _______.

3. Calculate these decimal multiplications:

a) 4.6 × 10 = _______

b) 0.35 × 100 = _______

c) 2.8 × 1,000 = _______

d) 0.007 × 100 = _______

4. Calculate these decimal divisions:

a) 45.2 ÷ 10 = _______

b) 830 ÷ 100 = _______

c) 6,500 ÷ 1,000 = _______

d) 92.4 ÷ 100 = _______

🚜 Part 2: Real-Life Problems (Manawatu Context)

5. A dairy farm in Feilding produces 45.6 litres of milk per day. How many litres would they produce in 10 days? Show your working.

6. The distance from Palmerston North to Ashhurst is 12.4 kilometres. Express this distance in metres by multiplying by 1,000.

7. A local farm weighs sheep feed in grams. If one bag contains 2,500 grams, what is the weight in kilograms? (Hint: divide by 1,000)

8. Challenge Problem: A farmer sells wool for $3.45 per kilogram. If the price increases by a factor of 10, then decreases by dividing by 100, what is the new price per kilogram?

🎯 Part 3: Pattern Recognition

9. Complete the pattern by filling in the missing numbers:

0.45 → 4.5 → _______ → 450 → _______

What operation is being performed at each step? _________________

10. Explain in your own words why multiplying by 1,000 moves the decimal point 3 places to the left:

11. Extension: If 0.0034 × 10,000 = 34, explain what happened to the decimal point and why:

Decimals and Powers Ten

Decimals and Powers of Ten

📊 Part 1: Moving the Decimal Point

🚜 Part 2: Real-Life Problems (Manawatu Context)

🎯 Part 3: Pattern Recognition

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