🔒 Why does 1 + 10**(-20) - 1 = 0

[weary canyon]

Hello I got a question why does 1 + 10**(-20) - 1 = 0 in Python?
When I print 1 + 10**(-20), the output is 1.
Couldn't find an answer on google or rather I don't know where to start looking.

[limber kayak]

@weary canyon

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[rocky flicker]

probably because 10^-20 is negligible

!e print(10**-20)

[limber kayak]

:white_check_mark: Your 3.12 eval job has completed with return code 0.

1e-20

[rocky flicker]

or maybe not

!e print(1 + 10**-20 - 1)

[limber kayak]

:white_check_mark: Your 3.12 eval job has completed with return code 0.

0.0

[rocky flicker]

yeah probably because it's negligible

!e print(1 - 1 + 10**-20)

[limber kayak]

:white_check_mark: Your 3.12 eval job has completed with return code 0.

1e-20

[weary canyon]

Huh interesting

[rocky flicker]

!e print(1 + 10**-20)

[limber kayak]

:white_check_mark: Your 3.12 eval job has completed with return code 0.

1.0

[weary canyon]

!e print(1 * 10**-20)

[limber kayak]

:white_check_mark: Your 3.12 eval job has completed with return code 0.

1e-20

[rocky flicker]

it's because 10^-20 is 0.000 000 000 000 000 000 01

yeah i know

[wheat lily]

floats have greater precision the closer to 0 they are, so it makes sense for 1e-20 to be representable but also for 1+ 1e-20 to not be representable

[weary canyon]

Ah thanks!

[limber kayak]

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🔒 Why does 1 + 10**(-20) - 1 = 0