# Overview 

There are a lot of decimals with infinite representations in binary. One such example is  `0.1`. It looks complicated in binary, but it is one of the simplest decimals. 

## The number `0.1` in binary
The number `0.1` can be represented in binary as `0.00011001100110011...`.
The pattern of `0011` repeats infinitely. We can't store the binary equivalent of decimal `0.1`.

As we know, `0.1` is equal to `1/10`. A binary of 10 is equal to `1010`. When we divide `1` by `1010` to show `0.1` as a bicimal, then the division process will never terminate. In other words, it will repeat forever. We can abort this division process by writing it as $0.0\overline{0011}$. 

## The number `0.1` in floating-point
The finite representation of `1/10` is $0.0\overline{0011}$, but it can’t be represented in floating-point because we can't deal with bars in floating-point. We can represent it only in fixed digits/bits using any data type. In floating-point, we can represent it using 53 bits. 


## Coding example 
Different data types can store different numbers of significant digits according to their storage capacity. The following example shows the number `0.1` in decimal and binary. We can truncate the value to the specific significant digits or bits.   

from decimal import Decimal
from fractions import Fraction
import bitstring

print("----Representing 0.1 in 17 significant digits----")
print(format(0.1, '.17g')) # 17 significant digits
print("----Representing 0.1 in decimal----")
print(Decimal.from_float(0.1))
print("----Representing 0.1 in decimal using 17 significant digits----")
print(format(Decimal.from_float(0.1), '.17')) # 17 significant digits
print("----Representing 0.1 in binary----")
bits = bitstring.BitArray(float=0.1, length=64) # 64 bits
print(bits.bin)

python

## Explanation
- Lines 1-3: We import different packages. 
- Line 6: We print `0.1` in 17 significant digits using the `format()` method. 
- Line 8: We print `0.1` using the `from_float()` method of the `Decimal` library. 
- Line 10: We print `0.1` in 17 significant digits using the `Decimal` library's function.
- Line 13: We print the value in binary using the `bitstring` library's function.

py.tar.gz

Why does 0.1 not exist in floating-point?

0.1 cannot be finitely stored in floating-point due to its infinite repeating binary representation (0.000110011...).

Why does 0.1 not exist in floating-point?

Overview

The number 0.1 in binary

The number 0.1 in floating-point

Coding example

Explanation

The number `0.1` in binary

The number `0.1` in floating-point