Python 2.7 division not showing exact result

Question

When I divide 1/5e-5 it gives the correct answer but 1/5e-6 gives an answer close to the correct one.

>>> 1/5e-5
20000.0
>>> 1/5e-6
199999.99999999997 (should be 200000)
>>>

How can I get it to show the exact value. I tried importing decimel, numpy and scipy but none of them change the result.

You should read up on [floating point rounding error](http://programmers.stackexchange.com/questions/101163/what-causes-floating-point-rounding-errors). The basic issue is that computers cannot exactly model certain decimal fractions in binary, much like we cannot model 2/3 (0.66667...) in decimal. — Nick White, Jan 27 '16 at 22:46
You can't always get an "exact value" with floating-point math. — TigerhawkT3, Jan 27 '16 at 22:47
Could you make use of the [fractions](https://docs.python.org/2/library/fractions.html) module? — jacob, Jan 27 '16 at 22:47
To get python to round the number to some level of precision, try [round(1/5e-6)](https://docs.python.org/2/library/functions.html#round) — Nick White, Jan 27 '16 at 22:48
I'm not sure that this is an exact dupe -- OP seems to be at least a little aware of the limitations of floating point mathematics (based on the attempts to use `decimal`, `scipy`, `numpy`, ...). The question is if there is any way to work-around the limitations of floating point math to get an exact answer. It seems to me that it should be possible with decimal or fractions . . . — mgilson, Jan 27 '16 at 22:51
@NickWhite rounding doesn't help, because most perfectly exact decimals simply can't be represented in binary. You can round it 100 times but you still get the same almost-but-not-quite answer. — Mark Ransom, Jan 27 '16 at 23:33

score 2 · Accepted Answer · answered Jan 27 '16 at 22:49

2

You can get decimal to do this properly -- You just have to avoid using floating point numbers along the way:

>>> import decimal
>>> decimal.Decimal('1') / (decimal.Decimal('5') / decimal.Decimal('1000000'))
Decimal('2E+5')

answered Jan 27 '16 at 22:49

mgilson

You can use floating point numbers converted to `Decimal`, as long as they're exact. Integers converted to floating point will meet this requirement as long as they're less than `2**53`. – Mark Ransom Jan 27 '16 at 23:35

1 Answers1