For each of the following expressions, what value will the expression give? Verify your answers

For each of the following expressions, what value will the...

Key Concepts

Parentheses Usage

Parentheses in expressions are used to explicitly define the order of operations, overriding the default operator precedence. This allows for grouping parts of an expression together to ensure that they are computed first, which is crucial for obtaining the intended result.

Operator Precedence

Operator precedence dictates the order in which operations are evaluated in an expression. In Python, multiplication, division, and modulus are evaluated before addition and subtraction unless parentheses are used to alter the natural order, ensuring that expressions yield predictable results.

Division Operators

Division in Python, using the '/' operator, produces a floating-point result even when both operands are integers. This concept highlights the importance of understanding how numerical types affect the outcome of an arithmetic operation, especially when precision is a concern.

Arithmetic Operators

Arithmetic operators in Python include subtraction (-), multiplication (*), division (/), and modulus (%). These operators are used to perform basic arithmetic computations, and their behavior depends on the types of operands involved (integers or floats).

Modulus Operator

The modulus operator (%) computes the remainder of the division of one number by another. Its behavior, especially with negative numbers, is defined in Python such that the result has the same sign as the divisor, making it important to grasp its rules for accurate computations.

Transcript

00:01 So here we want to figure out what these expressions result in in python and we will verify it by running it inside a python environment.

00:11 So one of the things you might notice here is that we're gonna evaluate it for both python 2 and python 3 and there will be some differences actually.

00:18 And the reason why is that many textbooks and in particular the textbook which has this exercise uses python 2 because in the time that it was written, while python 3 was out already, python 2 was still the most used version.

00:35 But nowadays python 3 is much much more common than python 2.

00:38 In fact, python 2 is what we would refer to as being sunsetted.

00:43 So something that's soon, you know, like the community will be not supporting python 2 anymore.

00:53 Okay, so the first thing that we want to evaluate is 9 minus 3 and that would just work with, you know, common arithmetic.

01:01 9 minus 3 is 6.

01:03 The next is 8 times 2 .5.

01:06 So the way i like to think about it, we have to do 8 times 2 which is 16 plus 8 times 0 .5 which is 4.

01:15 So 16 plus 4 which should give us 20.

01:19 And for both python 2 and python 3 that would also give us 20.

01:22 And in particular because we are multiplying an int and the float together and floats in theory, floats are a superset of ints.

01:36 So like every int can be represented as a float but not vice versa.

01:40 So float is sort of the bigger set here, which means that our answer will be a float not an int.

01:46 So it will be 20 .0 and the point 0 indicates that it's a float not an int.

01:51 Okay, now here we see the difference, right? so here we are doing 9 divided by 2 both of which are integers.

02:00 So in python 2 it results in an integer.

02:03 So 9 divided by 2 is 4 .5 and the way that python turns that into an integer is that it rounds down.

02:10 So 4 .5 rounded down is 4.

02:15 Now python 3 says, well, it's 4 .5.

02:18 So it's 4 .5 and it will represent it as a float.

02:23 Now 9 divided by negative 2, that's negative 4 .5, right? in python 2 again, these are both integers.

02:31 So the result will be an integer and negative 4 .5 rounded down.

02:37 So this is a little bit more tricky, right? if you draw the number line, right? so this is negative 5.

02:41 This is negative 4.

02:43 This is negative 4 .5.

02:45 So if we round down this should be negative 5.

02:49 And in python 3 again, it's negative 4 .5.

02:53 So python 3 doesn't bother with keeping it an integer despite both operands being integers.

03:00 So it stays negative 4 .5.

03:04 Okay, now we have sort of this other operator, which is an inner common arithmetic, but it's very useful for computer programming language, computer programming, which is the modulo operator.

03:16 So this is the operator.

03:19 You can think about this as a remainder operator, right? so if we divide 9 by 2, what is the remainder? it will be 1.

03:27 And in python 3, it will be the same.

03:29 It will be 1.

03:30 Now, if we divide 9 by negative 2, right? so what is 9 divided by negative 2? it's going to be negative, you know, to get the closest you can to 9, you would multiply negative 2 by negative 4 to get 8.

03:49 And the remainder is 1.

03:51 But in python, the second operator, sorry, the second operand determines the sign of the modulo result.

04:04 So 9 mod negative 2 is negative 1 rather than 1.

04:08 And that's the same in python 3.

04:11 Now, negative 9 mod 2, again, the sign is taken from the second operand.

04:18 If you divide negative 9 by 2, it's not an even number, so it doesn't have remainder 0.

04:23 It's an odd number, so it must have remainder 1.

04:26 And again, the sign is going to be positive because 2, which is the second operand, is positive.

04:32 So it will be 1.

04:34 Now, 9 divided by negative 2 .0, and the difference between this and this, these two, or sorry, rather these two, is that this now is a float.

04:46 So the result, right? so this is an integer divided by a float.

04:49 So the result will be a float in both python 2 and python 3.

04:54 So here we have negative 4 .5 and negative 4 .5, which are both floats.

05:01 And finally, here, these last two sort of demonstrate order of operations, right? if you guys remember order of operations in grade school, it's pemdas, where multiplication comes before addition...

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