Numbers and Maths 🔢

Two kinds of number

crew = 12          # int: a whole number
speed = 9.5        # float: a number with a decimal point

print(type(crew))
print(type(speed))

<class 'int'>
<class 'float'>

int is short for integer, meaning whole. float is short for floating point, which refers to the decimal point being able to move around. That is the whole distinction, and it matters more than it looks.

print(2 ** 100)

1267650600228229401496703205376

The operators

print(7 / 2)
print(7 // 2)
print(7 % 2)
print(7 ** 2)
print(10 / 5)      # still a float, even though it divides exactly

3.5
3
1
49
2.0

The two division signs are worth your attention

// and % look like curiosities. They are two of the most useful operators in programming.

total_minutes = 137

hours = total_minutes // 60      # how many whole hours fit
minutes = total_minutes % 60     # what is left over

print(f"{total_minutes} minutes is {hours}h {minutes}m")

137 minutes is 2h 17m

That pattern converts seconds to clocks, pennies to pounds, and items to pages.

% also answers "is this divisible by":

for number in [10, 15, 21, 30]:
    if number % 5 == 0:
        print(f"{number} divides by 5 exactly")
    else:
        print(f"{number} does not")

10 divides by 5 exactly
15 divides by 5 exactly
21 does not
30 divides by 5 exactly

"Remainder is zero" is how you test for even numbers (n % 2 == 0), how you make something happen every tenth time round a loop, and how you write FizzBuzz, the most famous interview question there is.

Order of operations

print(2 + 3 * 4)        # multiplication happens first
print((2 + 3) * 4)      # brackets win
print(2 ** 3 ** 2)      # powers go right to left: 2 ** 9

14
20
512

The rules are the ones you learned at school. The advice is simpler than the rules: use brackets whenever there is the slightest doubt. They cost nothing and they are free documentation.

The 0.1 + 0.2 scandal

print(0.1 + 0.2)

0.30000000000000004

Computers store floats in binary. In binary, one tenth is a recurring number, exactly as one third is recurring in decimal (0.3333...). You have to stop writing digits somewhere, so the stored value is very slightly off, and the errors add up. The standard that defines this behaviour is IEEE 754, published in 1985 and implemented by essentially every CPU on earth.

What to actually do about it:

# 1. Never compare floats with ==
print(0.1 + 0.2 == 0.3)

# 2. Compare with a tolerance instead
import math
print(math.isclose(0.1 + 0.2, 0.3))

# 3. Round for display
print(round(0.1 + 0.2, 2))

# 4. For money, use exact decimal arithmetic
from decimal import Decimal
print(Decimal("0.1") + Decimal("0.2"))

False
True
0.3
0.3

Rule of thumb: floats for measurements, Decimal for money, ints for counting. Financial software that uses floats for currency is a bug with a launch party.

Converting between types

print(int("42") + 1)        # text to whole number
print(float("3.5") + 1)     # text to decimal
print(str(42) + " crabs")   # number to text
print(int(9.99))            # float to int: chops, does not round
print(round(9.99))          # this is what you usually wanted

43
4.5
42 crabs
9
10

The maths module

import math

print(math.sqrt(144))
print(math.pi)
print(math.floor(9.99), math.ceil(9.01))
print(math.factorial(5))

12.0
3.141592653589793
9 10
120

import loads a module: a file of code somebody else already wrote and tested. math ships with Python. Lesson 20 covers imports properly, but you can use them now with no ceremony.

bill = 87.50
people = 4
tip_rate = 0.15

tip = bill * tip_rate
total = bill + tip
each = total / people

print(f"Bill:  {bill:.2f}")
print(f"Tip:   {tip:.2f}")
print(f"Total: {total:.2f}")
print(f"Each:  {each:.2f}")

Bill:  87.50
Tip:   13.12
Total: 100.62
Each:  25.16

total = 9384

hours = total // 3600
remainder = total % 3600
minutes = remainder // 60
seconds = remainder % 60

print(f"{hours}h {minutes}m {seconds}s")
print(f"{hours:02d}:{minutes:02d}:{seconds:02d}")

2h 36m 24s
02:36:24

print(17 // 5)
print(-17 // 5)
print(17 % 5)
print(-17 % 5)