# Ruby Language Numbers

## Numbers hierarchy

Ruby includes several built-in classes to represent numbers:

Numeric
Integer
Fixnum    # 1
Bignum    # 10000000000000000000
Float       # 1.0
Complex     # (1+0i)
Rational    # Rational(2, 3) == 2/3
BigDecimal  # not loaded by default

The most common are:

• Fixnum to represent, for instance positive and negative integers
• Float to represent floating point numbers

BigDecimal is the only one not loaded by default. You can load it with:

require "bigdecimal"

Note that in ruby 2.4+, Fixnum and Bignum are unified; all integers are now just members of the Integer class. For backwards compatibility, Fixnum == Bignum == Integer.

## Creating an Integer

0       # creates the Fixnum 0
123     # creates the Fixnum 123
1_000   # creates the Fixnum 1000. You can use _ as separator for readability

By default the notation is base 10. However, there are some other built-in notations for different bases:

0xFF    # Hexadecimal representation of 255, starts with a 0x
0b100   # Binary representation of 4, starts with a 0b
0555    # Octal representation of 365, starts with a 0 and digits

## Converting a String to Integer

You can use the Integer method to convert a String to an Integer:

Integer("123")      # => 123
Integer("0xFF")     # => 255
Integer("0b100")    # => 4
Integer("0555")     # => 365

You can also pass a base parameter to the Integer method to convert numbers from a certain base

Integer('10', 5)    # => 5
Integer('74', 8)    # => 60
Integer('NUM', 36)  # => 30910

Note that the method raises an ArgumentError if the parameter cannot be converted:

Integer("hello")
# raises ArgumentError: invalid value for Integer(): "hello"
Integer("23-hello")
# raises ArgumentError: invalid value for Integer(): "23-hello"

You can also use the String#to_i method. However, this method is slightly more permissive and has a different behavior than Integer:

"23".to_i         # => 23
"23-hello".to_i   # => 23
"hello".to_i      # => 0

String#to_i accepts an argument, the base to interpret the number as:

"10".to_i(2) # => 2
"10".to_i(3) # => 3
"A".to_i(16) # => 10

## Converting a number to a string

Fixnum#to_s takes an optional base argument and represents the given number in that base:

2.to_s(2)   # => "10"
3.to_s(2)   # => "11"
3.to_s(3)   # => "10"
10.to_s(16) # => "a"

If no argument is provided, then it represents the number in base 10

2.to_s # => "2"
10423.to_s # => "10423"

## Dividing two numbers

When dividing two numbers pay attention to the type you want in return. Note that dividing two integers will invoke the integer division. If your goal is to run the float division, at least one of the parameters should be of float type.

Integer division:

3 / 2 # => 1

Float division

3 / 3.0 # => 1.0

16 / 2 / 2    # => 4
16 / 2 / 2.0  # => 4.0
16 / 2.0 / 2  # => 4.0
16.0 / 2 / 2  # => 4.0

## Rational Numbers

Rational represents a rational number as numerator and denominator:

r1 = Rational(2, 3)
r2 = 2.5.to_r
r3 = r1 + r2
r3.numerator   # => 19
r3.denominator # => 6
Rational(2, 4) # => (1/2)

Other ways of creating a Rational

Rational('2/3')  # => (2/3)
Rational(3)      # => (3/1)
Rational(3, -5)  # => (-3/5)
Rational(0.2)    # => (3602879701896397/18014398509481984)
Rational('0.2')  # => (1/5)
0.2.to_r         # => (3602879701896397/18014398509481984)
0.2.rationalize  # => (1/5)
'1/4'.to_r       # => (1/4)

## Complex Numbers

1i     # => (0+1i)
1.to_c # => (1+0i)
rectangular = Complex(2, 3)  # => (2+3i)
polar       = Complex('[email protected]') # => (-0.4161468365471424+0.9092974268256817i)

polar.rectangular # => [-0.4161468365471424, 0.9092974268256817]
rectangular.polar # => [3.605551275463989, 0.982793723247329]
rectangular + polar # => (1.5838531634528576+3.909297426825682i)

## Even and Odd Numbers

The even? method can be used to determine if a number is even

4.even?      # => true
5.even?      # => false

The odd? method can be used to determine if a number is odd

4.odd?       # => false
5.odd?       # => true

## Rounding Numbers

The round method will round a number up if the first digit after its decimal place is 5 or higher and round down if that digit is 4 or lower. This takes in an optional argument for the precision you're looking for.

4.89.round        # => 5
4.25.round        # => 4
3.141526.round(1) # => 3.1
3.141526.round(2) # => 3.14
3.141526.round(4) # => 3.1415

Floating point numbers can also be rounded down to the highest integer lower than the number with the floor method

4.9999999999999.floor # => 4

They can also be rounded up to the lowest integer higher than the number using the ceil method

4.0000000000001.ceil  # => 5