Place Value Expanded Notation Worksheet - Free Printable

Let’s go step by step to write each number in expanded notation.

Expanded notation means breaking the number into parts based on place value — like how much each digit is worth depending on where it sits (ones, tens, hundreds, tenths, etc.).

We’ll use multiplication for each digit times its place value, just like the examples:
- 731 = 7×100 + 3×10 + 1×1
- 56.23 = 5×10 + 6×1 + 2×1/10 + 3×1/100

Now let’s do each problem one at a time.

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1. 21,781

Break it down:

- 2 is in the ten-thousands → 2 × 10,000
- 1 is in the thousands → 1 × 1,000
- 7 is in the hundreds → 7 × 100
- 8 is in the tens → 8 × 10
- 1 is in the ones → 1 × 1

So:
2×10,000 + 1×1,000 + 7×100 + 8×10 + 1×1

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2. 867,230

Digits and places:

- 8 → hundred-thousands → 8 × 100,000
- 6 → ten-thousands → 6 × 10,000
- 7 → thousands → 7 × 1,000
- 2 → hundreds → 2 × 100
- 3 → tens → 3 × 10
- 0 → ones → 0 × 1 (we can skip writing this since it’s zero)

So:
8×100,000 + 6×10,000 + 7×1,000 + 2×100 + 3×10

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3. 2,713,948

Places from left to right:

- 2 → millions → 2 × 1,000,000
- 7 → hundred-thousands → 7 × 100,000
- 1 → ten-thousands → 1 × 10,000
- 3 → thousands → 3 × 1,000
- 9 → hundreds → 9 × 100
- 4 → tens → 4 × 10
- 8 → ones → 8 × 1

So:
2×1,000,000 + 7×100,000 + 1×10,000 + 3×1,000 + 9×100 + 4×10 + 8×1

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4. 19,325,836

Break it down:

- 1 → ten-millions → 1 × 10,000,000
- 9 → millions → 9 × 1,000,000
- 3 → hundred-thousands → 3 × 100,000
- 2 → ten-thousands → 2 × 10,000
- 5 → thousands → 5 × 1,000
- 8 → hundreds → 8 × 100
- 3 → tens → 3 × 10
- 6 → ones → 6 × 1

So:
1×10,000,000 + 9×1,000,000 + 3×100,000 + 2×10,000 + 5×1,000 + 8×100 + 3×10 + 6×1

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5. 511,506,392

This is a big one! Let’s go digit by digit:

- 5 → hundred-millions → 5 × 100,000,000
- 1 → ten-millions → 1 × 10,000,000
- 1 → millions → 1 × 1,000,000
- 5 → hundred-thousands → 5 × 100,000
- 0 → ten-thousands → 0 × 10,000 → skip
- 6 → thousands → 6 × 1,000
- 3 → hundreds → 3 × 100
- 9 → tens → 9 × 10
- 2 → ones → 2 × 1

So:
5×100,000,000 + 1×10,000,000 + 1×1,000,000 + 5×100,000 + 6×1,000 + 3×100 + 9×10 + 2×1

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6. 3,419.3

Now we have decimals!

Whole number part: 3,419

- 3 → thousands → 3 × 1,000
- 4 → hundreds → 4 × 100
- 1 → tens → 1 × 10
- 9 → ones → 9 × 1

Decimal part: .3 → that’s 3 tenths → 3 × 1/10

So:
3×1,000 + 4×100 + 1×10 + 9×1 + 3×1/10

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7. 56,340.21

Whole number: 56,340

- 5 → ten-thousands → 5 × 10,000
- 6 → thousands → 6 × 1,000
- 3 → hundreds → 3 × 100
- 4 → tens → 4 × 10
- 0 → ones → 0 × 1 → skip

Decimal: .21

- 2 → tenths → 2 × 1/10
- 1 → hundredths → 1 × 1/100

So:
5×10,000 + 6×1,000 + 3×100 + 4×10 + 2×1/10 + 1×1/100

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8. 45.219

Whole number: 45

- 4 → tens → 4 × 10
- 5 → ones → 5 × 1

Decimal: .219

- 2 → tenths → 2 × 1/10
- 1 → hundredths → 1 × 1/100
- 9 → thousandths → 9 × 1/1000

So:
4×10 + 5×1 + 2×1/10 + 1×1/100 + 9×1/1000

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9. 2.846

Whole number: 2 → 2 × 1

Decimal: .846

- 8 → tenths → 8 × 1/10
- 4 → hundredths → 4 × 1/100
- 6 → thousandths → 6 × 1/1000

So:
2×1 + 8×1/10 + 4×1/100 + 6×1/1000

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10. 20,519.31

Whole number: 20,519

- 2 → ten-thousands → 2 × 10,000
- 0 → thousands → 0 × 1,000 → skip
- 5 → hundreds → 5 × 100
- 1 → tens → 1 × 10
- 9 → ones → 9 × 1

Decimal: .31

- 3 → tenths → 3 × 1/10
- 1 → hundredths → 1 × 1/100

So:
2×10,000 + 5×100 + 1×10 + 9×1 + 3×1/10 + 1×1/100

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✔ All done! Now here are the final answers neatly listed:

Final Answer:
21,781 = 2×10,000 + 1×1,000 + 7×100 + 8×10 + 1×1
867,230 = 8×100,000 + 6×10,000 + 7×1,000 + 2×100 + 3×10
2,713,948 = 2×1,000,000 + 7×100,000 + 1×10,000 + 3×1,000 + 9×100 + 4×10 + 8×1
19,325,836 = 1×10,000,000 + 9×1,000,000 + 3×100,000 + 2×10,000 + 5×1,000 + 8×100 + 3×10 + 6×1
511,506,392 = 5×100,000,000 + 1×10,000,000 + 1×1,000,000 + 5×100,000 + 6×1,000 + 3×100 + 9×10 + 2×1
3,419.3 = 3×1,000 + 4×100 + 1×10 + 9×1 + 3×1/10
56,340.21 = 5×10,000 + 6×1,000 + 3×100 + 4×10 + 2×1/10 + 1×1/100
45.219 = 4×10 + 5×1 + 2×1/10 + 1×1/100 + 9×1/1000
2.846 = 2×1 + 8×1/10 + 4×1/100 + 6×1/1000
20,519.31 = 2×10,000 + 5×100 + 1×10 + 9×1 + 3×1/10 + 1×1/100