Float

A Float object stores a real number using the native architecture’s double-precision floating-point representation.

Float Imprecisions

Some real numbers can be represented precisely as Float objects:

37.5    # => 37.5
98.75   # => 98.75
12.3125 # => 12.3125

Others cannot; among these are the transcendental numbers, including:

• Pi, π: in mathematics, a number of infinite precision: 3.1415926535897932384626433… (to 25 places); in Ruby, it is of limited precision (in this case, to 16 decimal places):

  Example

  Run in Playground

  Math::PI # => 3.141592653589793
  

• Euler’s number, e: in mathematics, a number of infinite precision: 2.7182818284590452353602874… (to 25 places); in Ruby, it is of limited precision (in this case, to 15 decimal places):

  Example

  Run in Playground

  Math::E # => 2.718281828459045
  

Some floating-point computations in Ruby give precise results:

1.0/2   # => 0.5
100.0/8 # => 12.5

Others do not:

• In mathematics, 2/3 as a decimal number is an infinitely-repeating decimal: 0.666… (forever); in Ruby, 2.0/3 is of limited precision (in this case, to 16 decimal places):

  Example

  Run in Playground

  2.0/3 # => 0.6666666666666666
  

• In mathematics, the square root of 2 is an irrational number of infinite precision: 1.4142135623730950488016887… (to 25 decimal places); in Ruby, it is of limited precision (in this case, to 16 decimal places):

  Example

  Run in Playground

  Math.sqrt(2.0) # => 1.4142135623730951
  

• Even a simple computation can introduce imprecision:

  Example

  Run in Playground

  x = 0.1 + 0.2 # => 0.30000000000000004
  y = 0.3       # => 0.3
  x == y        # => false
  

See:

• docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

• github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#user-content–why-are-rubys-floats-imprecise

• en.wikipedia.org/wiki/Floating_point#Accuracy_problems

Note that precise storage and computation of rational numbers is possible using Rational objects.

Creating a Float

You can create a Float object explicitly with:

• A floating-point literal.

You can convert certain objects to Floats with:

• Method Float.

What’s Here

First, what’s elsewhere. Class Float:

• Inherits from class Numeric and class Object.

• Includes module Comparable.

Here, class Float provides methods for:

• Querying

• Comparing

• Converting

Querying

• finite?: Returns whether self is finite.

• hash: Returns the integer hash code for self.

• infinite?: Returns whether self is infinite.

• nan?: Returns whether self is a NaN (not-a-number).

Comparing

• <: Returns whether self is less than the given value.

• <=: Returns whether self is less than or equal to the given value.

• <=>: Returns a number indicating whether self is less than, equal to, or greater than the given value.

• == (aliased as === and eql?): Returns whether self is equal to the given value.

• >: Returns whether self is greater than the given value.

• >=: Returns whether self is greater than or equal to the given value.

Converting

• % (aliased as modulo): Returns self modulo the given value.

• *: Returns the product of self and the given value.

• **: Returns the value of self raised to the power of the given value.

• +: Returns the sum of self and the given value.

• -: Returns the difference of self and the given value.

• /: Returns the quotient of self and the given value.

• ceil: Returns the smallest number greater than or equal to self.

• coerce: Returns a 2-element array containing the given value converted to a Float and self

• divmod: Returns a 2-element array containing the quotient and remainder results of dividing self by the given value.

• fdiv: Returns the Float result of dividing self by the given value.

• floor: Returns the greatest number smaller than or equal to self.

• next_float: Returns the next-larger representable Float.

• prev_float: Returns the next-smaller representable Float.

• quo: Returns the quotient from dividing self by the given value.

• round: Returns self rounded to the nearest value, to a given precision.

• to_i (aliased as to_int): Returns self truncated to an Integer.

• to_s (aliased as inspect): Returns a string containing the place-value representation of self in the given radix.

• truncate: Returns self truncated to a given precision.