Converting Standard Form Numbers to Expanded Form (4-Digit Numbers ... - Free Printable

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, explaining how to break down the number into its component parts (hundreds, tens, ones, tenths, hundredths, thousandths, etc.).

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1) 327.328

Given:
= 3×100 + 2×10 + 7×1 + 3×0.1 + 2×0.01 + 8×0.001
✔ Already correct.

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2) 24.79

Break down:
- 2 is in the tens place → 2 × 10
- 4 is in the ones place → 4 × 1
- 7 is in the tenths place → 7 × 0.1
- 9 is in the hundredths place → 9 × 0.01

So:
= 2 × 10 + 4 × 1 + 7 × 0.1 + 9 × 0.01

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3) 1.275

- 1 is in the ones place → 1 × 1
- 2 is in the tenths → 2 × 0.1
- 7 is in the hundredths → 7 × 0.01
- 5 is in the thousandths → 5 × 0.001

= 1 × 1 + 2 × 0.1 + 7 × 0.01 + 5 × 0.001

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4) 943.7

- 9 = hundreds → 9 × 100
- 4 = tens → 4 × 10
- 3 = ones → 3 × 1
- 7 = tenths → 7 × 0.1

= 9 × 100 + 4 × 10 + 3 × 1 + 7 × 0.1

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5) 82.73

- 8 = tens → 8 × 10
- 2 = ones → 2 × 1
- 7 = tenths → 7 × 0.1
- 3 = hundredths → 3 × 0.01

= 8 × 10 + 2 × 1 + 7 × 0.1 + 3 × 0.01

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6) 0.726

- 7 = tenths → 7 × 0.1
- 2 = hundredths → 2 × 0.01
- 6 = thousandths → 6 × 0.001

= 7 × 0.1 + 2 × 0.01 + 6 × 0.001

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7) 6.81

- 6 = ones → 6 × 1
- 8 = tenths → 8 × 0.1
- 1 = hundredths → 1 × 0.01

= 6 × 1 + 8 × 0.1 + 1 × 0.01

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8) 532.95

- 5 = hundreds → 5 × 100
- 3 = tens → 3 × 10
- 2 = ones → 2 × 1
- 9 = tenths → 9 × 0.1
- 5 = hundredths → 5 × 0.01

= 5 × 100 + 3 × 10 + 2 × 1 + 9 × 0.1 + 5 × 0.01

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9) 27.381

- 2 = tens → 2 × 10
- 7 = ones → 7 × 1
- 3 = tenths → 3 × 0.1
- 8 = hundredths → 8 × 0.01
- 1 = thousandths → 1 × 0.001

= 2 × 10 + 7 × 1 + 3 × 0.1 + 8 × 0.01 + 1 × 0.001

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10) 9.127

- 9 = ones → 9 × 1
- 1 = tenths → 1 × 0.1
- 2 = hundredths → 2 × 0.01
- 7 = thousandths → 7 × 0.001

= 9 × 1 + 1 × 0.1 + 2 × 0.01 + 7 × 0.001

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11) 723.59

- 7 = hundreds → 7 × 100
- 2 = tens → 2 × 10
- 3 = ones → 3 × 1
- 5 = tenths → 5 × 0.1
- 9 = hundredths → 9 × 0.01

= 7 × 100 + 2 × 10 + 3 × 1 + 5 × 0.1 + 9 × 0.01

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12) 9.378

- 9 = ones → 9 × 1
- 3 = tenths → 3 × 0.1
- 7 = hundredths → 7 × 0.01
- 8 = thousandths → 8 × 0.001

= 9 × 1 + 3 × 0.1 + 7 × 0.01 + 8 × 0.001

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13) 48.125

- 4 = tens → 4 × 10
- 8 = ones → 8 × 1
- 1 = tenths → 1 × 0.1
- 2 = hundredths → 2 × 0.01
- 5 = thousandths → 5 × 0.001

= 4 × 10 + 8 × 1 + 1 × 0.1 + 2 × 0.01 + 5 × 0.001

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14) 75.023

- 7 = tens → 7 × 10
- 5 = ones → 5 × 1
- 0 = tenths → 0 × 0.1 (can be omitted, but we include for completeness)
- 2 = hundredths → 2 × 0.01
- 3 = thousandths → 3 × 0.001

= 7 × 10 + 5 × 1 + 0 × 0.1 + 2 × 0.01 + 3 × 0.001
(Or simply: 7 × 10 + 5 × 1 + 2 × 0.01 + 3 × 0.001)

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15) 803.27

- 8 = hundreds → 8 × 100
- 0 = tens → 0 × 10
- 3 = ones → 3 × 1
- 2 = tenths → 2 × 0.1
- 7 = hundredths → 7 × 0.01

= 8 × 100 + 0 × 10 + 3 × 1 + 2 × 0.1 + 7 × 0.01
(Or: 8 × 100 + 3 × 1 + 2 × 0.1 + 7 × 0.01)

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16) 19.205

- 1 = tens → 1 × 10
- 9 = ones → 9 × 1
- 2 = tenths → 2 × 0.1
- 0 = hundredths → 0 × 0.01
- 5 = thousandths → 5 × 0.001

= 1 × 10 + 9 × 1 + 2 × 0.1 + 0 × 0.01 + 5 × 0.001
(Or: 1 × 10 + 9 × 1 + 2 × 0.1 + 5 × 0.001)

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17) 384.157

- 3 = hundreds → 3 × 100
- 8 = tens → 8 × 10
- 4 = ones → 4 × 1
- 1 = tenths → 1 × 0.1
- 5 = hundredths → 5 × 0.01
- 7 = thousandths → 7 × 0.001

= 3 × 100 + 8 × 10 + 4 × 1 + 1 × 0.1 + 5 × 0.01 + 7 × 0.001

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18) 940.29

- 9 = hundreds → 9 × 100
- 4 = tens → 4 × 10
- 0 = ones → 0 × 1
- 2 = tenths → 2 × 0.1
- 9 = hundredths → 9 × 0.01

= 9 × 100 + 4 × 10 + 0 × 1 + 2 × 0.1 + 9 × 0.01
(Or: 9 × 100 + 4 × 10 + 2 × 0.1 + 9 × 0.01)

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19) 612.092

- 6 = hundreds → 6 × 100
- 1 = tens → 1 × 10
- 2 = ones → 2 × 1
- 0 = tenths → 0 × 0.1
- 9 = hundredths → 9 × 0.01
- 2 = thousandths → 2 × 0.001

= 6 × 100 + 1 × 10 + 2 × 1 + 0 × 0.1 + 9 × 0.01 + 2 × 0.001
(Or: 6 × 100 + 1 × 10 + 2 × 1 + 9 × 0.01 + 2 × 0.001)

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20) 53.284

- 5 = tens → 5 × 10
- 3 = ones → 3 × 1
- 2 = tenths → 2 × 0.1
- 8 = hundredths → 8 × 0.01
- 4 = thousandths → 4 × 0.001

= 5 × 10 + 3 × 1 + 2 × 0.1 + 8 × 0.01 + 4 × 0.001

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✔ Final Answers:

1) 3×100 + 2×10 + 7×1 + 3×0.1 + 2×0.01 + 8×0.001
2) 2 × 10 + 4 × 1 + 7 × 0.1 + 9 × 0.01
3) 1 × 1 + 2 × 0.1 + 7 × 0.01 + 5 × 0.001
4) 9 × 100 + 4 × 10 + 3 × 1 + 7 × 0.1
5) 8 × 10 + 2 × 1 + 7 × 0.1 + 3 × 0.01
6) 7 × 0.1 + 2 × 0.01 + 6 × 0.001
7) 6 × 1 + 8 × 0.1 + 1 × 0.01
8) 5 × 100 + 3 × 10 + 2 × 1 + 9 × 0.1 + 5 × 0.01
9) 2 × 10 + 7 × 1 + 3 × 0.1 + 8 × 0.01 + 1 × 0.001
10) 9 × 1 + 1 × 0.1 + 2 × 0.01 + 7 × 0.001
11) 7 × 100 + 2 × 10 + 3 × 1 + 5 × 0.1 + 9 × 0.01
12) 9 × 1 + 3 × 0.1 + 7 × 0.01 + 8 × 0.001
13) 4 × 10 + 8 × 1 + 1 × 0.1 + 2 × 0.01 + 5 × 0.001
14) 7 × 10 + 5 × 1 + 2 × 0.01 + 3 × 0.001
15) 8 × 100 + 3 × 1 + 2 × 0.1 + 7 × 0.01
16) 1 × 10 + 9 × 1 + 2 × 0.1 + 5 × 0.001
17) 3 × 100 + 8 × 10 + 4 × 1 + 1 × 0.1 + 5 × 0.01 + 7 × 0.001
18) 9 × 100 + 4 × 10 + 2 × 0.1 + 9 × 0.01
19) 6 × 100 + 1 × 10 + 2 × 1 + 9 × 0.01 + 2 × 0.001
20) 5 × 10 + 3 × 1 + 2 × 0.1 + 8 × 0.01 + 4 × 0.001

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🔍 Key Concept:

Expanded form shows the value of each digit based on its place value:
- Hundreds: ×100
- Tens: ×10
- Ones: ×1
- Tenths: ×0.1
- Hundredths: ×0.01
- Thousandths: ×0.001

You can ignore zero digits if they don’t contribute (e.g., 0 × 0.1), but including them is acceptable too.

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