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#computer-arithmetic
## Definition
> [!tldr] Definition
> An [[Integers|integer]] is written in **base 10** or **decimal** format if it consists of a string of digits, all between $0$ and $9$, that represent groupings of power of 10.
## Examples
Base 10 is the standard way of writing positive [[integers]] we learn in school. The digits represent place value. For example the [[Integers|integer]] $267$ has 7 in the "ones place", 6 in the "tens place", and 2 in the "hundreds place". This means that this number consists of 2 copies or groups of $100$, 6 copies of $10$, and 7 copies of $1$. We can write this fact as:
$267 = 2 \times 100 + 6 \times 10 + 7 \times 1$
Each of the groups is represented by a power of 10, so we can also write this as:
$267 = 2 \times 10^2 + 6 \times 10^1 + 7 \times 10^0$
**Another example:** The number $90125$, written in base 10, can be written as
$90125 = 9 \times 10^4 + 0 \times 10^3 + 1 \times 10^2 + 2 \times 10^1 + 5 \times 10^0$
The digit attached to each grouping of 10 must be a [[Natural numbers|natural number]] between $0$ and $9$. If a digit were greater than 9, it would just create a new place value.
## Resources
The first three minutes of this video covers more on base 10 representation:
<div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/575905500?badge=0&autopause=0&player_id=0&app_id=58479" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 1.1: Base 10 and Base 2 representation of integers"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script>