Advanced Arithmetic
A step beyond basics: learn how Python handles floor division and modulo (including negatives) and get a quick tour of the built-in math module you'll use for everyday numeric work.
Floor Division (//)
Returns the floor of the exact quotient β i.e., rounds down toward ββ.
12print(7 // 3) # 2 print(-7 // 3) # -3 (floors down: -2.333... β -3)
Why it matters: indexing chunks/pages, time splitting (hours from seconds), and any "how many full groups fit" calculation.
Modulo %
Gives the remainder in the identity:
a == (a // b) * b + (a % b)
In Python, the remainder has the same sign as the divisor b.
123print(7 % 3) # 1 print(-7 % 3) # 2 (because -7 == (-3)*3 + 2) print(7 % -3) # -2 (because 7 == (-2)*(-3) + -2)
Why it matters: "every Nth" item, wrap-around (e.g., clock arithmetic), cycling through buckets.
Quick Note on Rounding
Built-in round(x, ndigits) uses "round half to even".
12print(round(2.5), round(3.5)) # 2 4 print(round(2.675, 2)) # 2.67 (binary float nuance)
The math Module (essentials)
Import once and access many handy functions/constants.
123456import math print(math.floor(2.9), math.ceil(2.1), math.trunc(-2.9)) # 2 3 -2 print(math.sqrt(9)) # 3.0 print(math.pi, math.e) # 3.14159... 2.71828... print(math.isfinite(1.0), math.isfinite(float('inf'))) # True False
floor/ceil/trunc: down / up / toward zero (watch negatives);sqrt: square root (float result);pi,e: common constants;isfinite,isnan,isinf: sanity checks for special float values.
1. What value will this code output?
2. What value will this code output?
3. Which call returns -3?
Thanks for your feedback!
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A step beyond basics: learn how Python handles floor division and modulo (including negatives) and get a quick tour of the built-in math module you'll use for everyday numeric work.
Floor Division (//)
Returns the floor of the exact quotient β i.e., rounds down toward ββ.
12print(7 // 3) # 2 print(-7 // 3) # -3 (floors down: -2.333... β -3)
Why it matters: indexing chunks/pages, time splitting (hours from seconds), and any "how many full groups fit" calculation.
Modulo %
Gives the remainder in the identity:
a == (a // b) * b + (a % b)
In Python, the remainder has the same sign as the divisor b.
123print(7 % 3) # 1 print(-7 % 3) # 2 (because -7 == (-3)*3 + 2) print(7 % -3) # -2 (because 7 == (-2)*(-3) + -2)
Why it matters: "every Nth" item, wrap-around (e.g., clock arithmetic), cycling through buckets.
Quick Note on Rounding
Built-in round(x, ndigits) uses "round half to even".
12print(round(2.5), round(3.5)) # 2 4 print(round(2.675, 2)) # 2.67 (binary float nuance)
The math Module (essentials)
Import once and access many handy functions/constants.
123456import math print(math.floor(2.9), math.ceil(2.1), math.trunc(-2.9)) # 2 3 -2 print(math.sqrt(9)) # 3.0 print(math.pi, math.e) # 3.14159... 2.71828... print(math.isfinite(1.0), math.isfinite(float('inf'))) # True False
floor/ceil/trunc: down / up / toward zero (watch negatives);sqrt: square root (float result);pi,e: common constants;isfinite,isnan,isinf: sanity checks for special float values.
1. What value will this code output?
2. What value will this code output?
3. Which call returns -3?
Thanks for your feedback!
