Place Value Calculator
Expanded form expresses a number as the sum of each digit multiplied by its place value. For example, 4,523 = 4,000 + 500 + 20 + 3 = (4 × 1000) + (5 × 100) + (2 × 10) + (3 × 1). It reinforces understanding of the base-10 number system.
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Tip: Expanded form is the foundation of the standard multiplication algorithm. 23 × 45 = (20+3) × (40+5) = 800 + 100 + 120 + 15 = 1,035.
- 1Identify the place value of each digit (ones, tens, hundreds, thousands...)
- 2Multiply each digit by its place value
- 3Write as a sum of these products
- 4Expanded notation: 4,523 = 4 × 10³ + 5 × 10² + 2 × 10¹ + 3 × 10⁰
7,304=7,000 + 300 + 0 + 4(7×1000) + (3×100) + (0×10) + (4×1)
0.536=0.5 + 0.03 + 0.006(5×0.1) + (3×0.01) + (6×0.001)
| Place | Value | Example digit in 4,523 |
|---|---|---|
| Thousands | 1,000 | 4 → 4,000 |
| Hundreds | 100 | 5 → 500 |
| Tens | 10 | 2 → 20 |
| Ones | 1 | 3 → 3 |
| Tenths | 0.1 | — |
| Hundredths | 0.01 | — |
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Fun Fact
The base-10 number system (decimal) likely developed because humans have 10 fingers. The Babylonians used base-60 (for time and angles), the Mayans used base-20, and computers use base-2 (binary).
References
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