Place Value Calculator and Expanded Form

How it works

Value of a digit = digit × its place value · place values: … 1,000 · 100 · 10 · 1 . 0.1 · 0.01 · 0.001 … (each place is 10 times the one to its right)

In our base-10 (decimal) number system the position of a digit sets its value: each place is worth ten times the place to its right. The ones, tens and hundreds repeat inside each period (thousands, millions, billions, trillions), and to the right of the decimal point come tenths, hundredths, thousandths and so on. Expanded form writes a number as the sum of each non-zero digit’s value; expanded notation shows the same sum as digit × place value or digit × power of 10, the forms used in primary and middle-school maths.

Worked example

For 4,507.36 the 4 is in the thousands place (4,000), 5 in the hundreds (500), 0 in the tens (0), 7 in the ones (7), 3 in the tenths (0.3) and 6 in the hundredths (0.06). Expanded form: 4,000 + 500 + 7 + 0.3 + 0.06. With powers of 10: (4 × 10³) + (5 × 10²) + (7 × 10⁰) + (3 × 10⁻¹) + (6 × 10⁻²).

Sources: Positional notation — Wikipedia · Place value — Math is Fun

Frequently asked questions