If your inputs are "sometimes" ints and "sometimes" floats then just wrap each input in a float(). You could make something more complex, but why would you?

input returns a string:

>>> x = input()
5.0
>>> x
'5.0'

If this string contains a representation of a number and you want to use it as a number, you need to call an appropriate function to parse the string and determine what number it represents:

>>> float(x)
5.0

However if the string doesn't represent a number, or if it doesn't represent a number of the type you're trying to convert it to, you will get an error:

>>> int(x)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: invalid literal for int() with base 10: '5.0'

(Technically 5.0 is an integer, but typically we think of '5.0' as representing not the number 5.0 itself but as representing some unknown number which would round to 5.0, i.e. some number between 4.95 and 5.05. Hence the failure to convert to an integer.)

And of course if the string doesn't represent a number at all, all of this is right out.

>>> float('banana')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: could not convert string to float: 'banana'

EDIT: 0x5453 raises a good point in the comments, which is that prior to python 3 the language would do these string-to-number conversions implicitly in some cases, which may be what you're remembering.

I don't understand why you don't just use floats?

while True:
            try:
                time = float(raw_input("How much time has elapsed since your last stop (in hours)?"))
            except ValueError:
                print("Enter a valid number of hours!")
                continue

By typing an integer value, it'll just turn it into a float anyway.

TLDR: Convert your input using ast.literal_eval first.

The return type of input in Python3 is always str. Checking it against type(2.2) (aka float) and type(2) (aka int) thus cannot succeed.

>>> number = input()
3
>>> number, type(number)
('3', <class 'str'>)

The simplest approach is to explicitly ask Python to convert your input. ast.literal_eval allows for save conversion to Python's basic data types. It automatically parses int and float literals to the correct type.

>>> import ast
>>> number = ast.literal_eval(input())
3
>>> number, type(number)
(3, <class 'int'>)

In your original code, apply ast.literal_eval to the user input. Then your type checks can succeed:

import ast

number = ast.literal_eval(input("Please input your number...... \n"))
if type(number) is float:
    print("Entered number is float and it's hexadecimal number is:", float.hex(number)) 
elif type(number) is int:
    print("Entered number is, ", number,"and it's hexadecimal number is:", hex(number)) 
else:
    print("you entered an invalid type")

Eagerly attempting to convert the input also means that your program might receive input that is not valid, as far as the converter is concerned. In this case, instead of getting some value of another type, an exception will be raised. Use try-except to respond to this case:

import ast

try:
    number = ast.literal_eval(input("Please input your number...... \n"))
except Exception as err:
    print("Your input cannot be parsed:", err)
else:
    if type(number) is float:
        print("Entered number is float and it's hexadecimal number is:", float.hex(number)) 
    elif type(number) is int:
        print("Entered number is, ", number, "and it's hexadecimal number is:", hex(number)) 
    else:
        print("you entered an invalid type")

It has nothing about utility, it has to do with what are the possible range of values you're program should/needs to accept.

If it needs to accept both integers and floats as inputs, then you should convert to float since floats can represent the integers.

But if you're program requires that the input be specifically an integer, then you should be casting to int.

EDIT:

In your example, you should always be using float, since money has a decimal value.

If you were asking "How many bananas did you buy?" You'd want to convert to int since those values are going to be 0, 1, 2, 3, 4, .... And then when you ask "How much did you pay for these bananas?" You'd want to convert to float since those inputs can range from 3.15, .77, 1, 1.00, ... etc.

It looks like you just want to make sure the value passed in can be operated upon like a float, regardless of whether the input is 3 or 4.79 for example, correct? If that's the case, then just cast the input as a float before operating on it.

Here's your modified code:

def aud_brl(amount, From, to):
    ER = 0.42108 
    if From.strip() == 'aud' and to.strip() == 'brl': 
        result = amount/ER 
    elif From.strip() == 'brl' and to.strip() == 'aud': 
        result = amount*ER 

    print(result)

def question(): 
    amount = float(input("Amount: "))
    From = input("From: ") 
    to = input("To: ")

    if (From == 'aud' or From == 'brl') and (to == 'aud' or to == 'brl'): 
        aud_brl(amount, From, to)

question()

I think that the simplest way to handle this is to check if the input string is numeric first:

https://www.tutorialspoint.com/python/string_isnumeric.htm

if input.isnumeric():
    print int(input)
else:
    try
        print float(input)
    except ValueError:
        # Do nothing

However if you can avoid exceptions completely the code would be better - exception handling can be quite expensive.

This answer to testing for an integer explains why exception handling can be expensive: https://stackoverflow.com/a/9859202/8358096

To avoid the second exception being hit regularly you could use the isalpha function mentioned below.

if input.isnumeric():
    print int(input)
else:
    if not input.isalpha():
        try
            print float(input)
        except ValueError:
            # Do nothing