Section · 01

The operators you'll use

Python has seven arithmetic operators. You’ve probably seen five of them since middle school:

3 + 2     # 5    — addition
3 - 2     # 1    — subtraction
3 * 2     # 6    — multiplication
3 / 2     # 1.5  — division (always returns a float)
3 ** 2    # 9    — exponent (3 squared)

And two that confuse newcomers:

7 // 2    # 3    — floor division (drops the decimal)
7 % 2     # 1    — modulo (the remainder)

//is “divide and throw away the decimal.” %is “what’s left over.” They’re cousins: 7 // 2 == 3 and 7 % 2 == 1 because 7 = 3 × 2 + 1. You’ll use both surprisingly often.

Section · 02

Order of operations (PEMDAS, but Python)

Python uses the same rules you learned in algebra: parentheses first, then exponents, then multiply/divide, then add/subtract. Left to right within a tier.

2 + 3 * 4         # 14   — multiplication first
(2 + 3) * 4       # 20   — parentheses change the order
2 ** 3 * 2        # 16   — exponent first: 8 * 2
10 - 4 + 1        # 7    — left to right: (10 - 4) + 1

Use parentheses even when you don’t need them, if it makes the intent clearer:

# Both produce the same result; the second one reads in one pass:
subtotal + subtotal * tax_rate
subtotal + (subtotal * tax_rate)

Three minutes of extra parentheses can save your reviewer twenty minutes of double-checking.

Section · 03

Where modulo earns its keep

% looks niche at first but solves a surprising number of real problems. Four examples worth remembering:

1. “Is this number divisible by N?”

# Run cleanup every 10th request
if request_count % 10 == 0:
    run_cleanup()

2. “Is it even or odd?”

if year % 2 == 0:
    print("even year")
else:
    print("odd year")

3. Time math (seconds → minutes and seconds)

total_seconds = 197
minutes = total_seconds // 60   # 3
seconds = total_seconds % 60    # 17
print(f"{minutes}:{seconds:02d}")  # "3:17"

4. Wrapping around a list

# Cycle through 5 colors for a chart
colors = ["red", "blue", "green", "purple", "orange"]
for i in range(12):
    color = colors[i % 5]   # 0,1,2,3,4,0,1,2,3,4,0,1
    draw_bar(color)

That last pattern shows up everywhere: rotating UI states, dealing cards, scheduling. Modulo is the answer to “wrap around when you hit the end.”

Section · 04

The floating-point trap

Try this in any Python prompt:

>>> 0.1 + 0.2
0.30000000000000004

That’s not a Python bug. It’s how floats are stored in hardware on every modern computer. Some decimal numbers can’t be represented exactly in binary — same way 1/3can’t be written exactly in decimal (0.333...). For 90% of your code it won’t matter. For the other 10% — money, scientific measurements, anything where exact equality matters — you need a different tool.

For displaying floats: round()

>>> round(0.1 + 0.2, 2)
0.3

For money: use Decimal or integer cents

# Bad: storing dollars as floats
total = 0.0
for item in cart:
    total += item.price       # rounding errors accumulate

# Better: store everything in cents (integers)
total_cents = 0
for item in cart:
    total_cents += item.price_cents
dollars = total_cents / 100   # only convert at the end

# Or use Decimal for full precision
from decimal import Decimal
total = Decimal("0.00")
for item in cart:
    total += Decimal(item.price_str)

Don’t use == on floats. Use abs(a - b) < 0.0001if you need to ask “close enough?” instead.

Numbers and operators, plus the floating-point trap that bites everyone once.