Lesson 2 · Python data types deep dive

Python Floats Explained: Precision, Rounding & Pitfalls | Data Types #2

Video two of the twelve-part series: the second numeric type, and where it genuinely diverges from int. Every literal form, every operator, the precision…

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CoursePython data types deep dive
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Python Data Types Deep-Dive, Video 2: Floats (float)#

Video two of the twelve-part series: the second numeric type, and where it genuinely diverges from int.
Every literal form, every operator, the precision problem that trips up nearly every beginner, and all seven public float methods.
Let's get into it.

Part 1: What Makes float Different#

temperature = 98.6
negative_float = -3.14
scientific = 6.022e23
print(type(temperature))
print(scientific)

<class 'float'>
6.022e+23

Part 2: Float Literals#

a = 3.14159
b = .5
c = 5.
d = 1_234.567_8
e = 1.5e-3
f = 1.5E10
print(a, b, c, d, e, f)

3.14159 0.5 5.0 1234.5678 0.0015 15000000000.0

Part 3: Arithmetic Operators#

a, b = 7.5, 2.0
print(a + b)
print(a - b)
print(a * b)
print(a / b)
print(a // b)
print(a % b)
print(a ** b)
print(5 + 2.0)

9.5
5.5
15.0
3.75
3.0
1.5
56.25
7.0

Part 4: The Precision Problem#

print(0.1 + 0.2)
print(0.1 + 0.2 == 0.3)
print(f'{0.1:.20f}')
print(f'{0.3:.20f}')

0.30000000000000004
False
0.10000000000000000555
0.29999999999999998890

import math
print(math.isclose(0.1 + 0.2, 0.3))
print(round(0.1 + 0.2, 10) == round(0.3, 10))

True
True

Part 5: Comparison Operators#

print(3.5 < 5.1)
print(5.0 == 5)
print(1.0 < 5.5 < 10.0)
print(float('inf') > 999999999999.9)

True
True
True
True

Part 6: Converting Values to float#

print(float('3.14'))
print(float('  3.14  '))
print(float('1e3'))
print(float(5))
print(float(True))
print(float('inf'))
print(float('-inf'))
print(float('nan'))

3.14
3.14
1000.0
5.0
1.0
inf
-inf
nan

try:
    float('not a number')
except ValueError as e:
    print(f'Caught: {e}')

Caught: could not convert string to float: 'not a number'

Part 7: Built-in Functions That Work With float#

print(abs(-3.7))
print(round(2.5))
print(round(3.5))
print(round(2.675, 2))
print(pow(2.0, 0.5))
print(min(3.1, 2.9, 4.4))
print(max(3.1, 2.9, 4.4))
print(sum([1.1, 2.2, 3.3]))

3.7
2
4
2.67
1.4142135623730951
2.9
4.4
6.6

Part 8: is_integer()#

print((5.0).is_integer())
print((5.5).is_integer())
print((-3.0).is_integer())
print((0.0).is_integer())

True
False
True
True

Part 9: as_integer_ratio()#

print((0.5).as_integer_ratio())
print((0.25).as_integer_ratio())
print((0.1).as_integer_ratio())
print((2.0).as_integer_ratio())

(1, 2)
(1, 4)
(3602879701896397, 36028797018963968)
(2, 1)

Part 10: hex()#

value = 3.14159
print(value.hex())
print((1.0).hex())
print((0.5).hex())
print((0.0).hex())

0x1.921f9f01b866ep+1
0x1.0000000000000p+0
0x1.0000000000000p-1
0x0.0p+0

Part 11: fromhex()#

value = 3.14159
hex_string = value.hex()
reconstructed = float.fromhex(hex_string)
print(reconstructed)
print(reconstructed == value)
print(float.fromhex('0x1.8p+1'))

3.14159
True
3.0

Part 12: real and imag#

value = 3.14
print(value.real)
print(value.imag)
print(type(value.real))

3.14
0.0
<class 'float'>

Part 13: conjugate()#

print((3.14).conjugate())
print((-2.5).conjugate())

3.14
-2.5

Part 14: Special Values: inf, -inf, and nan#

positive_infinity = float('inf')
negative_infinity = float('-inf')
not_a_number = float('nan')
print(positive_infinity)
print(1 / positive_infinity)
print(positive_infinity + 1)
print(positive_infinity == negative_infinity)
print(not_a_number == not_a_number)

inf
0.0
inf
False
False

import math
print(math.isnan(not_a_number))
print(math.isinf(positive_infinity))
print(math.isfinite(3.14))
print(0.0 / 1.0)
try:
    1.0 / 0.0
except ZeroDivisionError as e:
    print(f'Caught: {e}')

True
True
True
0.0
Caught: float division by zero

Part 15: Formatting Floats#

value = 1234.56789
print(f'{value:.2f}')
print(f'{value:.0f}')
print(f'{value:,.2f}')
print(f'{value:e}')
print(f'{value:.2e}')
print(f'{0.4567:.1%}')
print(f'{value:12.2f}')
print(f'{value:+.2f}')

1234.57
1235
1,234.57
1.234568e+03
1.23e+03
45.7%
     1234.57
+1234.57

Part 16: Rounding Pitfalls in Depth#

for value in [0.5, 1.5, 2.5, 3.5, 4.5, 5.5]:
    print(f'{value} rounds to {round(value)}')

0.5 rounds to 0
1.5 rounds to 2
2.5 rounds to 2
3.5 rounds to 4
4.5 rounds to 4
5.5 rounds to 6

from decimal import Decimal, ROUND_HALF_UP
value = Decimal('2.5')
print(value.quantize(Decimal('1'), rounding=ROUND_HALF_UP))
price_a = Decimal('19.99')
price_b = Decimal('5.01')
print(price_a + price_b)

3
25.00

Part 17: Immutability#

value = 3.14
print(id(value))
value = value + 1.0
print(id(value))

2542658413680
2542660158224

Part 18: Common Patterns and Pitfalls#

total = 0.0
for _ in range(10):
    total += 0.1
print(total)
print(total == 1.0)
import math
print(math.isclose(total, 1.0))

0.9999999999999999
False
True

def safe_range(start, stop, step):
    values = []
    current = start
    count = 0
    while count < round((stop - start) / step):
        values.append(round(current, 10))
        current += step
        count += 1
    return values
print(safe_range(0.0, 1.0, 0.1))

[0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]

Wrap-Up: What You Learned#

Float literals: decimal point, scientific notation, underscores, leading and trailing dots.
Arithmetic operators, and why mixing int and float always promotes to float.
The precision problem: why 0.1 + 0.2 != 0.3, and using math.isclose or decimal instead.
Converting to float with float(), including inf, -inf, and nan strings.
Built-in functions and banker's rounding: why round(2.5) is 2, not 3.
All seven public float methods: is_integer, as_integer_ratio, hex, fromhex, real, imag, and conjugate.
The three IEEE special values: inf, -inf, and nan, and how to test for each correctly.
Formatting floats, rounding pitfalls, immutability, and why real money math needs the decimal module.
Next up: complex numbers, the third and final built-in numeric type.

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