One half

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One half
One-half.svg
prefixes hemi- (from Greek)

semi-/demi- (from Latin)

Binary 0.1 or 0.011111111111...
Decimal 0.5 or 0.499999999999...
Dozenal 0.6 or 0.5BBBBBBBBBBBB...
Hexadecimal 0.8 or 0.7FFFFFFFFFFF...
Continued fraction [0; 1, 1] or [0; 2]
Single-precision

floating point

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. Conversely, division by one half is equivalent to multiplication by two, or "doubling". It appears often in mathematical equations, recipes, measurements, etc. Half can also be said to be one part of something divided into two equal parts.

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 )].

The Riemann hypothesis states that every nontrivial complex root of the Riemann zeta function has a real part equal to ½.

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.

Particularities in writing and language[edit]

Postal stamp, Ireland, 1940: one halfpenny postage due.

½ is also one of the few fractions to get a key of its own on typewriters (see fractions). It also gets its own point in some early extensions of ASCII at 171; and in Unicode, it gets its own code point at U+00BD (decimal 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 half is as well 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.

See also[edit]