Floats

2. Basic Types: Numbers

Floats

You might have noticed that division was the only operator to return a number with a fractional component or decimal, for example instead of . You might think what's the big deal, aren't these numbers the same? In a mathematical sense, yes, but for your computer, no. The difference being that decimals are stored differently in computer memory. We call the datatype that includes decimals $\color{#4271ae} {\mathtt{\text{float}}}$ , which is short for floating point number.

Floating point formatThe floating point format is a computer number format that represents a wide dynamic range of real numbers as approximations to support a trade-off between range and precision.

First, let's take a look at the multiple ways of declaring a $\color{#4271ae} {\mathtt{\text{float}}}$ .

Declaring a floatThe simplest way to declare a float is to add a fractional component to the desired number, if there's a zero before or after the decimal point you can choose to omit the zero:

>>> 1.0

1.0

>>> 1.

1.0

>>> .1

0.1

Using scientific notation

Scientific notation is the most concise way to declare very large or very small numbers in Python. Using scientific notation will always return a $\color{#4271ae} {\mathtt{\text{float}}}$ . Note that $\color{#F5871F} {\mathtt{\text{1e9}}}$ and $\color{#F5871F} {\mathtt{\text{1e+9}}}$ are both valid notations for the same floating point number.

>>> 1e0

1.0

>>> 1e+9

1000000000.0

>>> 1e-4

0.0001

Using casting

Casting is a way of explicitly converting an object to a different type, accepting the potential data loss in doing so. For casting to and between integers and floats we use the following functions:

Function Definition

$\color{#4271ae} {\mathtt{int}}(\textit{object}), \hspace{1em} \color{#4271ae}{\mathtt{float}}(\textit{object})$

Where the $\textit{object}$ argument can be of any Python type that supports casting to $\color{#4271ae} {\mathtt{\text{int}}}$ or $\color{#4271ae} {\mathtt{\text{float}}}$ .

Now, we can cast an $\color{#4271ae} {\mathtt{\text{int}}}$ to a $\color{#4271ae} {\mathtt{\text{float}}}$ and vice-versa. However, when casting a $\color{#4271ae} {\mathtt{\text{float}}}$ to an $\color{#4271ae} {\mathtt{\text{int}}}$ the numbers behind the decimal point are forever lost, the casting can't be reversed.

>>> float(1)

1.0

>>> int(1.8)

Since floats are more complicated to store than integers, there's a limit to the numbers the $\color{#4271ae} {\mathtt{\text{float}}}$ type can represent. When you enter a number that's bigger than the maximum (or smaller than the minimum) size $\color{#4271ae} {\mathtt{\text{float}}}$ can represent, Python will return $\mathtt{\text{inf}}$ , which stands for infinity. $\mathtt{\text{inf}}$ is a special $\color{#4271ae} {\mathtt{\text{float}}}$ that represents the absolute largest value that $\color{#4271ae} {\mathtt{\text{float}}}$ can accomodate.

For example, $1\times 10^{999}$ is a number that's too big for the $\color{#4271ae} {\mathtt{\text{float}}}$ format.

>>> 1e999

inf

This is similar for a value like $-1\times 10^{999}$ :

>>> -1e999

-inf

Values that exceed the limits of $\color{#4271ae} {\mathtt{\text{float}}}$ can still be used in expressions, but the value that is actually used is truncated to the special $\mathtt{\text{inf}}$ value. Which means that all the numbers that too large are equal. This is the same for negative numbers.

>>> 1e999 > 1e998

False

>>> 1e999 == 1e998

True

Floats support the same operators that integers do, but when an equation includes a $\color{#4271ae} {\mathtt{\text{float}}}$ , it will return a $\color{#4271ae} {\mathtt{\text{float}}}$ .

Exactly the same usage:

>>> 1.0 + 1.0

2.0

When mixing $\color{#4271ae} {\mathtt{\text{float}}}$ and $\color{#4271ae} {\mathtt{\text{int}}}$ typings in an expression, the expression will always return a $\color{#4271ae} {\mathtt{\text{float}}}$ .

>>> 1.0 + 1

2.0