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Decimal Expanded Form
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Decimal Expanded Form
📍 Part 1: Place Value and Powers of 10
1. What is the value of the digit 7 in the decimal number 4.72?
7 ones
7 tenths
7 hundredths
7 thousandths
2. Which of these shows the correct expanded form for 3.45?
3 × 10¹ + 4 × 10⁰ + 5 × 10⁻¹
3 × 10⁰ + 4 × 10⁻¹ + 5 × 10⁻²
3 × 10² + 4 × 10¹ + 5 × 10⁰
3 + 4 + 5
3. What decimal number is represented by: 2 × 10⁰ + 8 × 10⁻¹ + 3 × 10⁻²?
2.83
283
28.3
0.283
4. Which power of 10 represents the hundredths place?
10⁰
10⁻¹
10⁻²
10²
✏️ Part 2: Writing Expanded Form
5. Write 6.39 in expanded form using powers of 10:
6.39 = _____ × 10⁰ + _____ × 10⁻¹ + _____ × 10⁻²
6. Write 0.74 in expanded form using powers of 10:
0.74 = _____ × 10⁰ + _____ × 10⁻¹ + _____ × 10⁻²
7. Write 12.58 in expanded form using powers of 10:
8. Write 5.06 in expanded form using powers of 10:
🎯 Part 3: Extension Challenge
9. Write 7.284 in expanded form using powers of 10 (three decimal places):
10. What decimal number does this expanded form represent?
9 × 10⁰ + 0 × 10⁻¹ + 3 × 10⁻² + 7 × 10⁻³ = _________
11. Explain in your own words why we use negative powers of 10 for decimal places:
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