Numeric expressions

String expressions again

Earlier, you did some string expressions, like first_name + last_name. A string expression is some calculation that gives you a string result. You can put the result into a variable...

full_name = first_name + last_name

... output it...

print(first_name + last_name)

So we have:

String constants, like "There once was a ship that put to sea, ".
String variables, like ship_name.
String expressions, like 'The name of the ship was ' + ship_name.

Adela

Hey! I just noticed something. You can't look at a variable name, and tell whether it contains a string or a number.

Yes, you're right. It depends on how the variable is used. Here's some valid code:

ship_name = "Billy o' Tea"
first = "There once was a ship that put to sea,\n"
second = "And the name of the ship was the " + ship_name + ',\n'
final = first + second
print(final)

Reflect

What does that \n thing do in Python? You might need to look that one up.

If you were logged in as a student, the lesson would pause here, and you'd be asked to type in a response. If you want to try that out, ask for an account on this site.

Ethan

It lets you type the Enter key in a string.

Right! Want a g in your string, you type g. Want a z in your string, you type z. Want an Enter in your string, you type \n.

Run that code, and see what you get.

Here's what the Variable Explorer showed me:

Variable types

All four variables are strings.

A numeric expression gives you a numeric value, like meal_cost * 0.15.

We have:

Numeric constants, like 42.
Numeric variables, like the_ultimate_answer
Numeric expressions, like meal_cost * 0.15

Here's some code:

first = 2.4
second = 2.2
final = first + second
print(final)

Here's the Variable Explorer:

Variables

This time, first, second and final are all numbers, not strings.

Both programs have this line:

final = first + second

+ means something different in each program. In the first, it means "squoosh strings together." In the second, it means "add two numbers."

Numeric operators

The most common are:

Operator	Meaning
**	Raise to a power, e.g., 5**2 is 25
*	Multiply
/	Divide
+	Add
-	Subtract

As with regular arithmetic, operators have a precedence. Take this:

llama = 2 + 3**2 - 6/2 + 5*2 - 2**3

First, Python does the **, because it has the highest precedence. Python scans left to right, doing them in order.

llama = 2 + 9 - 6/2 + 5*2 - 2**3

Then the second **:

llama = 2 + 9 - 6/2 + 5*2 - 8

Next, Python does the * and /. They have equal priority, and are done left to right.

llama = 2 + 9 - 3 + 5*2 - 8

Then:

llama = 2 + 9 - 3 + 10 - 8

Now the + and -. They have equal priority, and are done left to right.

llama = 11 - 3 + 10 - 8
llama = 8 + 10 - 8
llama = 18 - 8
llama = 10

So, Python's built-in order is...

**, left to right, then...
* and /, left to right, then...
+ and -, left to right.

Another one:

cat = 3 - 5 + 2 * 2 ** 2 + 3

... would be done in this order...

3 - 5 + 2 * 2 ** 2 + 3 becomes 3 - 5 + 2 * 4 + 3
3 - 5 + 2 * 4 + 3 becomes 3 - 5 + 8 + 3
3 - 5 + 8 + 3 becomes -2 + 8 + 3
-2 + 8 + 3 becomes 6 + 3
6 + 3 becomes 9

Parentheses

You can use parentheses to change the order of operations. For example:

llama = (2 + 3)**2 - 6/2 + (5*2 - 2)**3

2 + 3 would be done first, then 5*2 - 2 (* first and then the -). The result is 534.

Rounding

Say you wanted to give someone a 5% discount on an item costing $2.95. A simple calculation:

final_price = 2.95 * 0.95
print('Final price: ' + final_price)

Reflect

What's the result?

If you were logged in as a student, the lesson would pause here, and you'd be asked to type in a response. If you want to try that out, ask for an account on this site.

Ray

It's 2.8025. So that's $2.80 plus a quarter of a cent.

Right. You wouldn't charge the quarter cent. Instead, you'd round the output value. The round function does that.

final_price = 2.95 * 0.95
print('Final price:' + str(round(final_price, 2)))

This one rounds to at most two decimal places.

It's better to round as late as possible in your code, just during output. That's what the code above does; round is in the print statement.

If you round earlier, you risk losing precision for later calculations.

Notice the code above doesn't change the value of final_price to 2.80. Only the display is affected. That's the right way to do it.

Run the code, and you'll get 2.8, not 2.80. You can force the missing 0, but let's not worry about it.

Your turn

Multiple choice

What would be printed?

print(2 + 3 * 4)

2 + 3 is 5, times 4 is 20, so 20.

2 + 3 * 4, the 3 * 4 first, then add 2: 14.

Either 14 or 20, depending on how the expression is run.

It depends on how Cthulhu is feeling.

Not graded. So why do it?

Multiple choice

What's this code output?

one = 2.2
two = 1.1
three = 1 + one / two / 2 * 4 - two / two + -1
print(three)

Work it out without running the code.

-1.0

3.0

About 12.5

Error.

Not graded. So why do it?

Multiple choice

What's this output?

cat = 2
pig = ((cat + 3) * 2 - 4) / 3
goat = 1 + pig / cat
cow = (goat - pig) * cat
print(goat/cow)

Try to work it out without running the code.

Error

Not graded. So why do it?

Multiple choice

What's this output?

ball = 3 % 2
glove = ball - -ball
bat = abs(ball - glove * 2)
bale = bat + glove + ball
stump = 12 / bale
print(stump + glove * 2 / glove - glove * ( bat - glove ) - glove)

You might need to look up a couple things, like: python '%'.

Try to work it out yourself, before running the code.

Error

Not graded. So why do it?

Multiple choice

What's this code output?

oz = 2 ** (7 - 5)
nz = oz ** abs(2 - oz)
png = 1 + (6 - (nz - oz) / (oz - 1 - 1))
fiji = 1 - png ** oz
print(fiji)

-255

-624

Error

Not graded. So why do it?

Exercise

Quadratic roots

Write a Python program to compute the roots of a quadratic equation. Here's one, let's call it Candice:

Quadratic equation

Solve it with this formula. We'll name it Billy:

Solution formula

Candice has two solutions. Billy gives both. See that +/- thing? For one solution, it's +. For the other, it's -. So, use Billy twice, once for each solution.

Ray

I don't remember much algebra.

You don't need to. Just get the inputs, and use the formula. You know all you need.

Here's some I/O:

a? 1
b? 6
c? 8
First solution: -2.0
Second solution: -4.0

For the square root, put this at the top of your code:

import math

Then you can compute square roots like this:

result = math.sqrt(something_goes_here)

Many quadratics don't have real roots, and will crash your program. Here's an example using 1 for a, b, and c:

Crashy

This is normal. Check the formula again, the bit under the square root:

What causes the trouble

If 4*a*c is more than b*b, you'll get a negative value. For example, when a, b, and c are all 1 (as in the screenshot), b*b - 4*a*c = 1*1 - 4*1*1 = -3.

Trying to find the square root of a negative value is a no-no in standard algebra. It does work when you use complex numbers, where the constant i is the square root of -1, but we're not going there.

Python's standard float type doesn't know what to do with the square root of a negative, and it crashes. That's OK, and expected.

To test your code, use values for a, b, and c that have real solutions. There's a useful page that lets you try different values for a, b, and c. Your program should produce the same results as the program on that page, except when 4*a*c is more than b*b. Here's what that page says when a, b, and c are all 1:

Complex roots

The roots are complex, so the values should crash your program.

However:

Real roots

Your program should produce the same roots, -4 and -2.

You'll learn a lot about data validation later in the course. You could use what you'll learn to avoid crashy crashy. But let's not worry about it for now.

Include comments for the IPO chunks.

Upload a zip of your project folder. The usual coding standards apply.

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