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I am trying to make a calculation: 100*e-6, but got wrong answer: 9.999999999999999e-05.
I also tried: 100*0.000001
All of them are not reasonable.

100*1e-6
Out[103]: 9.999999999999999e-05

100*0.000001
Out[104]: 9.999999999999999e-05

But 100*1e-5 is correct.

100*1e-5
Out[105]: 0.001

Many numbers cannot be exactly represented in the computer's floating point representation. So it stores as close as it can get.

You might be better off using format to display the number rounded to some decimal points.

>>> format(100*1e-6, "f")
'0.000100'
>>> format(100*1e-6, ".17f")
'0.00010000000000000'
>>> format(100*1e-6, ".20f")
'0.00009999999999999999'

or if you prefer exponential format...

>>> format(100*1e-6, "e")
'1.000000e-04'
>>> format(100*1e-6, ".11e")
'1.00000000000e-04'
>>> format(100*1e-6, ".15e")
'9.999999999999999e-05'

For background, https://docs.python.org/3.8/tutorial/floatingpoint.html

If you want to get into this in depth: https://en.wikipedia.org/wiki/Floating-point_arithmetic

I appreciate your reply to my problem. Your code and background are very useful for me.
Although I am still puzzled with "format(100*1e-6, ".15e") -->9.999999999999999e-05"...

(Jun-11-2020, 08:19 AM)bowlofred Wrote: [ -> ]Many numbers cannot be exactly represented in the computer's floating point representation. So it stores as close as it can get.

You might be better off using format to display the number rounded to some decimal points.

>>> format(100*1e-6, "f")
'0.000100'
>>> format(100*1e-6, ".17f")
'0.00010000000000000'
>>> format(100*1e-6, ".20f")
'0.00009999999999999999'

or if you prefer exponential format...

>>> format(100*1e-6, "e")
'1.000000e-04'
>>> format(100*1e-6, ".11e")
'1.00000000000e-04'
>>> format(100*1e-6, ".15e")
'9.999999999999999e-05'

For background, https://docs.python.org/3.8/tutorial/floatingpoint.html

The floating-point is a representation in binary system, which cannot represent all decimals.
It's mathematically proofed.

Decimal could help, but keep in mind, that it's much slower than floating-point arithmetic.

from decimal import Decimal

print(Decimal(100) * Decimal("1e-6"))
print(Decimal(100e6) * Decimal("1e-6"))

Output:
Decimal('0.000100')
Decimal('100.000000')

If you need floating-point with higher precision and fast, then try mpmath.
This will not eliminate the error, but you can get closer to a result.