Place Value Calculator
Place value is the system by which a digit's value depends on its position in a number. In 4,523: the 4 represents 4,000, the 5 represents 500, the 2 represents 20, and the 3 represents 3. Our base-10 system uses powers of 10 for each position.
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Tip: Teaching place value: use physical manipulatives (base-10 blocks). One unit cube = 1, a rod of 10 = 10, a flat of 100 = 100, a large cube = 1,000. Seeing the physical size difference makes the concept concrete.
- 1Each position is 10× the position to its right
- 2Ones → Tens → Hundreds → Thousands → Ten-Thousands...
- 3Decimal places go right: Tenths → Hundredths → Thousandths
- 4The digit 0 is crucial as a placeholder (502 ≠ 52)
| Position | Value | In 1,234,567.89 |
|---|---|---|
| Millions | 1,000,000 | 1 |
| Hundred-thousands | 100,000 | 2 |
| Ten-thousands | 10,000 | 3 |
| Thousands | 1,000 | 4 |
| Hundreds | 100 | 5 |
| Tens | 10 | 6 |
| Ones | 1 | 7 |
| Tenths | 0.1 | 8 |
| Hundredths | 0.01 | 9 |
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Fun Fact
Zero as a placeholder was independently invented by the Babylonians (~300 BCE), Mayans (~350 CE), and Indians (~500 CE). Without zero as a placeholder, you couldn't distinguish 52 from 502 from 5,002 — the number system wouldn't work.
References
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