One half
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| ½ | |
| prefixes | hemi- (from Greek) |
| Binary | 0.1 or 0.011111111111... |
| Decimal | 0.5 or 0.499999999999... |
| Hexadecimal | 0.8 or 0.7FFFFFFFFFFF... |
| Continued fraction | [0; 1, 1] or [0; 2] |
| Single-precision | 3F000000 (hex) =
00111111000000000000000000000000 (binary) |
One half is the irreducible fraction resulting from dividing one by two (½), or any number by its double; multiplication by one half is equivalent to division by two. It is the fraction occurring most often in mathematical equations, recipes, measurements, etc.
For instance, the area S of a triangle is computed
- S = ½ × base × perpendicular height
One half also figures in the formula for calculating figurate numbers, such as triangular numbers and pentagonal numbers:
- ½ × n [(s - 2) n - (4 - s)]
and in the formula for computing magic constants for magic squares
- M2(n) = ½ × [n (n2 + 1 )]
One half has two different decimal expansions, the familiar 0.5 and the recurring 0.49999999... It has a similar pair of expansions in any even base. It is a common trap to believe these expressions represent distinct numbers: see the proof that 0.999... equals 1 for detailed discussion of a related case.
One half is also:
- One of the few fractions to get a key of its own on typewriters. It also gets its own point in some early extensions of ASCII at 171; and in Unicode, it gets its own code point at 189 in the C1 Controls and Latin-1 Supplement block, and a cross-reference in the Number Forms block, which contains some other fractions.
- One of the few fractions which is commonly expressed in natural languages by suppletion rather than regular derivation; compare English one half with regular formations like one sixth from six.
