Expanded form math worksheet for converting numbers to their expanded decimal form.

Let's solve this step by step. The task is to write each number in expanded form, breaking it down into the value of each digit based on its place value.

We’ll go through each problem one by one, showing how to break down the number into:

- Hundreds, tens, ones
- Tenths (1/10), hundredths (1/100), thousandths (1/1000), etc.

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1) 327.328

Given:
= 3×100 + 2×10 + 7×1 + 3×(1/10) + 2×(1/100) + 8×(1/1000) ✔

This is correct.

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2) 24.79

Break it down:
- 2 × 10 = 20
- 4 × 1 = 4
- 7 × (1/10) = 0.7
- 9 × (1/100) = 0.09

So:
2 × 10 + 4 × 1 + 7 × ¹⁄₁₀ + 9 × ¹⁄₁₀₀

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3) 1.275

- 1 × 1 = 1
- 2 × (1/10) = 0.2
- 7 × (1/100) = 0.07
- 5 × (1/1000) = 0.005

So:
1 × 1 + 2 × ¹⁄₁₀ + 7 × ¹⁄₁₀₀ + 5 × ¹⁄₁₀₀₀

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4) 943.7

- 9 × 100 = 900
- 4 × 10 = 40
- 3 × 1 = 3
- 7 × (1/10) = 0.7

So:
9 × 100 + 4 × 10 + 3 × 1 + 7 × ¹⁄₁₀

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5) 82.73

- 8 × 10 = 80
- 2 × 1 = 2
- 7 × (1/10) = 0.7
- 3 × (1/100) = 0.03

So:
8 × 10 + 2 × 1 + 7 × ¹⁄₁₀ + 3 × ¹⁄₁₀₀

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6) 0.726

- 7 × (1/10) = 0.7
- 2 × (1/100) = 0.02
- 6 × (1/1000) = 0.006

So:
7 × ¹⁄₁₀ + 2 × ¹⁄₁₀₀ + 6 × ¹⁄₁₀₀₀

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7) 6.81

- 6 × 1 = 6
- 8 × (1/10) = 0.8
- 1 × (1/100) = 0.01

So:
6 × 1 + 8 × ¹⁄₁₀ + 1 × ¹⁄₁₀₀

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8) 532.95

- 5 × 100 = 500
- 3 × 10 = 30
- 2 × 1 = 2
- 9 × (1/10) = 0.9
- 5 × (1/100) = 0.05

So:
5 × 100 + 3 × 10 + 2 × 1 + 9 × ¹⁄₁₀ + 5 × ¹⁄₁₀₀

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9) 27.381

- 2 × 10 = 20
- 7 × 1 = 7
- 3 × (1/10) = 0.3
- 8 × (1/100) = 0.08
- 1 × (1/1000) = 0.001

So:
2 × 10 + 7 × 1 + 3 × ¹⁄₁₀ + 8 × ¹⁄₁₀₀ + 1 × ¹⁄₁₀₀₀

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10) 9.127

- 9 × 1 = 9
- 1 × (1/10) = 0.1
- 2 × (1/100) = 0.02
- 7 × (1/1000) = 0.007

So:
9 × 1 + 1 × ¹⁄₁₀ + 2 × ¹⁄₁₀₀ + 7 × ¹⁄₁₀₀₀

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11) 723.59

- 7 × 100 = 700
- 2 × 10 = 20
- 3 × 1 = 3
- 5 × (1/10) = 0.5
- 9 × (1/100) = 0.09

So:
7 × 100 + 2 × 10 + 3 × 1 + 5 × ¹⁄₁₀ + 9 × ¹⁄₁₀₀

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12) 9.378

- 9 × 1 = 9
- 3 × (1/10) = 0.3
- 7 × (1/100) = 0.07
- 8 × (1/1000) = 0.008

So:
9 × 1 + 3 × ¹⁄₁₀ + 7 × ¹⁄₁₀₀ + 8 × ¹⁄₁₀₀₀

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13) 48.125

- 4 × 10 = 40
- 8 × 1 = 8
- 1 × (1/10) = 0.1
- 2 × (1/100) = 0.02
- 5 × (1/1000) = 0.005

So:
4 × 10 + 8 × 1 + 1 × ¹⁄₁₀ + 2 × ¹⁄₁₀₀ + 5 × ¹⁄₁₀₀₀

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14) 75.023

- 7 × 10 = 70
- 5 × 1 = 5
- 0 × (1/10) = 0
- 2 × (1/100) = 0.02
- 3 × (1/1000) = 0.003

So:
7 × 10 + 5 × 1 + 0 × ¹⁄₁₀ + 2 × ¹⁄₁₀₀ + 3 × ¹⁄₁₀₀₀

> Note: Even if a digit is zero, we still include it in expanded form when required.

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15) 803.27

- 8 × 100 = 800
- 0 × 10 = 0
- 3 × 1 = 3
- 2 × (1/10) = 0.2
- 7 × (1/100) = 0.07

So:
8 × 100 + 0 × 10 + 3 × 1 + 2 × ¹⁄₁₀ + 7 × ¹⁄₁₀₀

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16) 19.205

- 1 × 10 = 10
- 9 × 1 = 9
- 2 × (1/10) = 0.2
- 0 × (1/100) = 0
- 5 × (1/1000) = 0.005

So:
1 × 10 + 9 × 1 + 2 × ¹⁄₁₀ + 0 × ¹⁄₁₀₀ + 5 × ¹⁄₁₀₀₀

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17) 384.157

- 3 × 100 = 300
- 8 × 10 = 80
- 4 × 1 = 4
- 1 × (1/10) = 0.1
- 5 × (1/100) = 0.05
- 7 × (1/1000) = 0.007

So:
3 × 100 + 8 × 10 + 4 × 1 + 1 × ¹⁄₁₀ + 5 × ¹⁄₁₀₀ + 7 × ¹⁄₁₀₀₀

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18) 940.29

- 9 × 100 = 900
- 4 × 10 = 40
- 0 × 1 = 0
- 2 × (1/10) = 0.2
- 9 × (1/100) = 0.09

So:
9 × 100 + 4 × 10 + 0 × 1 + 2 × ¹⁄₁₀ + 9 × ¹⁄₁₀₀

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19) 612.092

- 6 × 100 = 600
- 1 × 10 = 10
- 2 × 1 = 2
- 0 × (1/10) = 0
- 9 × (1/100) = 0.09
- 2 × (1/1000) = 0.002

So:
6 × 100 + 1 × 10 + 2 × 1 + 0 × ¹⁄₁₀ + 9 × ¹⁄₁₀₀ + 2 × ¹⁄₁₀₀₀

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20) 53.284

- 5 × 10 = 50
- 3 × 1 = 3
- 2 × (1/10) = 0.2
- 8 × (1/100) = 0.08
- 4 × (1/1000) = 0.004

So:
5 × 10 + 3 × 1 + 2 × ¹⁄₁₀ + 8 × ¹⁄₁₀₀ + 4 × ¹⁄₁₀₀₀

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## ✔ Final Answers:

1) 3×100 + 2×10 + 7×1 + 3×¹⁄₁₀ + 2×¹⁄₁₀₀ + 8×¹⁄₁₀₀₀
2) 2×10 + 4×1 + 7×¹⁄₁₀ + 9×¹⁄₁₀₀
3) 1×1 + 2×¹⁄₁₀ + 7×¹⁄₁₀₀ + 5×¹⁄₁₀₀₀
4) 9×100 + 4×10 + 3×1 + 7×¹⁄₁₀
5) 8×10 + 2×1 + 7×¹⁄₁₀ + 3×¹⁄₁₀₀
6) 7×¹⁄₁₀ + 2×¹⁄₁₀₀ + 6×¹⁄₁₀₀₀
7) 6×1 + 8×¹⁄₁₀ + 1×¹⁄₁₀₀
8) 5×100 + 3×10 + 2×1 + 9×¹⁄₁₀ + 5×¹⁄₁₀₀
9) 2×10 + 7×1 + 3×¹⁄₁₀ + 8×¹⁄₁₀₀ + 1×¹⁄₁₀₀₀
10) 9×1 + 1×¹⁄₁₀ + 2×¹⁄₁₀₀ + 7×¹⁄₁₀₀₀
11) 7×100 + 2×10 + 3×1 + 5×¹⁄₁₀ + 9×¹⁄₁₀₀
12) 9×1 + 3×¹⁄₁₀ + 7×¹⁄₁₀₀ + 8×¹⁄₁₀₀₀
13) 4×10 + 8×1 + 1×¹⁄₁₀ + 2×¹⁄₁₀₀ + 5×¹⁄₁₀₀₀
14) 7×10 + 5×1 + 0×¹⁄₁₀ + 2×¹⁄₁₀₀ + 3×¹⁄₁₀₀₀
15) 8×100 + 0×10 + 3×1 + 2×¹⁄₁₀ + 7×¹⁄₁₀₀
16) 1×10 + 9×1 + 2×¹⁄₁₀ + 0×¹⁄₁₀₀ + 5×¹⁄₁₀₀₀
17) 3×100 + 8×10 + 4×1 + 1×¹⁄₁₀ + 5×¹⁄₁₀₀ + 7×¹⁄₁₀₀₀
18) 9×100 + 4×10 + 0×1 + 2×¹⁄₁₀ + 9×¹⁄₁₀₀
19) 6×100 + 1×10 + 2×1 + 0×¹⁄₁₀ + 9×¹⁄₁₀₀ + 2×¹⁄₁₀₀₀
20) 5×10 + 3×1 + 2×¹⁄₁₀ + 8×¹⁄₁₀₀ + 4×¹⁄₁₀₀₀

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✔ All numbers are now written in expanded form, using place values (powers of 10 and fractions for decimals). Let me know if you'd like a printable version or explanation of any specific one!