### Code:

a = 0.1

b = 0.2

c = 0.3

print(a + b == c)

### Solution and Explanation:

The code snippet:

a = 0.1

b = 0.2

c = 0.3

print(a + b == c)

produces

**False**as output. This result can be surprising, but it stems from the way floating-point numbers are represented in computer hardware. Here’s a detailed explanation:### Floating-Point Representation

#### Binary Representation:

Computers represent floating-point numbers in binary (base-2) format, which can lead to precision issues because not all decimal fractions can be represented exactly as binary fractions.

For example, 0.1 in binary is an infinitely repeating sequence: 0.00011001100110011....

#### Precision Limitations:

When 0.1 and 0.2 are stored in a computer's memory, they are approximated to the nearest value that can be represented in the finite number of bits available.

The same approximation happens for 0.3.

#### Summation Inaccuracy:

When adding 0.1 and 0.2, the result is not exactly 0.3 due to these approximations. Instead, the result is a value very close to 0.3, but not exactly 0.3.

The actual value of a + b might be something like 0.30000000000000004.

#### Comparison:

When Python compares a + b to c, it is comparing 0.30000000000000004 (the result of a + b) to 0.3 (the stored value of c), and since these are not exactly equal, the comparison returns False.

### Demonstration with More Precision

You can observe this behavior by printing the values with higher precision:

print(f"{a + b:.17f}") # Shows the precision error

print(f"{c:.17f}")

This will output:

0.30000000000000004

0.29999999999999999

As you can see, the two numbers are very close but not exactly the same, which explains why the comparison a + b == c evaluates to False.

Best Practices

To avoid issues with floating-point comparisons:

#### Use a Tolerance:

Instead of direct comparison, use a small tolerance value to check if the numbers are "close enough":

tolerance = 1e-10

print(abs((a + b) - c) < tolerance) # True

#### Decimal Module:

For financial and other high-precision calculations, use Python's decimal module which can handle decimal arithmetic more accurately.

from decimal import Decimal

a = Decimal('0.1')

b = Decimal('0.2')

c = Decimal('0.3')

print(a + b == c) # True

This approach avoids the pitfalls of floating-point arithmetic by using a representation that can exactly represent decimal fractions.

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