Place and value
In the base-ten system, each position is worth ten times the position to its right. A digit's value is the digit times its place value: in 4,305.07 the 4 is in the thousands place, so it is worth 4 × 1,000 = 4,000. The 7 is in the hundredths place, so it is worth 7 × 0.01 = 0.07.
Expanded form writes the number as the sum of those values: 4,305.07 = 4 × 1,000 + 3 × 100 + 5 × 1 + 7 × 0.01 = 4,000 + 300 + 5 + 0.07. In powers of ten, it is 4 × 10³ + 3 × 10² + 5 × 10⁰ + 7 × 10⁻².
| Place | Value | Power of ten |
|---|---|---|
| thousands | 1,000 | 10³ |
| hundreds | 100 | 10² |
| tens | 10 | 10¹ |
| ones | 1 | 10⁰ |
| tenths | 0.1 | 10⁻¹ |
| hundredths | 0.01 | 10⁻² |
| thousandths | 0.001 | 10⁻³ |
From expanded form back to standard form
Switch modes to add up an expanded form such as 4 × 1000 + 3 × 100 + 5 × 1 + 7 × 0.01 or 6 × 10^3 + 2 × 10^-2. The terms are added as exact decimals, so the result is 4,305.07 or 6,000.02 with no rounding.
Limits
Numbers can have up to 15 digits before the decimal point and 12 after it. Names follow the short scale used in the US and UK, where a billion is 10⁹. Zero digits have no value but still hold their place; they are listed in the table and left out of the expanded form.