# Thousand

A thousand, written as 1,000, is a natural number that follows the number 999, and precedes the number 1,001. It can also be written as 10^{3}, in scientific notation as 1 × 10^{3}, or in a number of other ways, such as roman numerals. In writing, a thousand is also sometimes denoted with a "k":

- 1k = 1,000
- 10k = 10,000
- 100k = 100,000

The "k" can be seen as adding three 0's to the number it is attached to. It is also sometimes used as follows:

- 1kk = 1,000,000
- 1kkk = 1,000,000,000

The k equals 10^{3}, so "kk" is read as multiplying 10^{3} × 10^{3}.

When talking about measurements, such as kilometers, or the abbreviated version km, the "k" means the same thing as described above. It indicates one thousand, the same way that kilogram, kg, indicates 1,000 grams.

Example

What is 1,000 ÷ 1kk × 100k × 10?

1,000 ÷ 1,000,000 × 100,000 × 10 = 1,000 or 1k

## Place value

In the decimal numeral system, the value of a digit is given by the position of the digit relative to the decimal point. Specifically, each position represents a power of 10 by which the digit in the position is multiplied in order to get the value. For example, the thousands place is the position that is 3 digits left of the decimal point. 1,000 can be written as 1,000.0 just to illustrate its position relative to the decimal point. In 1,000.0, "1" is in the thousands place. If instead there were a 2 in the thousands place, we could write it in expanded form as:

2 × 10^{3} = 2,000

If there were other digits in the number, such as 2,200, the 3rd "2" from the right is in the hundreds place, and its value can similarly be calculated as 2 × 10^{2} = 100; the total value in expanded form is therefore:

2 × 10^{3} + 2 × 10^{2} = 2000 + 200 = 2200

On the other end of the decimal point, the thousandths place is 3 digits right of the decimal point. In 2000.001, the "1" is in the thousandths place, and its value could be written as 1 × 10^{-3}.

Understanding place value is important since it is the basis of the most widely used number system. Refer to the place value page for more information.