Definition:Digit

Definition

Let $n$ be a number expressed in a particular number base, $b$ for example.

Then $n$ can be expressed as:

$\sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0 . r_{-1} r_{-2} \ldots}_b$

where:

$m$ is such that $b^m \le n < b^{m+1}$;

all the $r_i$ are such that $0 \le r_i < b$.

Each of the $r_i$ are known as the digits of $n$ (base $b$).

Also known as

A digit can also be known as a figure, especially in natural language.

Hence the phrase to figure (something) out, which has the overtone of calculation by arithmetic.

Also see

• Definition:Digital

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): Glossary
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): digit
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): Glossary
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): digit
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): figure (in number)