# How to truncate/round-off decimal numbers?

Discussion in 'Python' started by Girish Sahani, Jun 20, 2006.

1. ### Girish SahaniGuest

Hi,

I want to truncate every number to 2 digits after the decimal point. I
tried the following but it doesnt work.

>>> a = 2
>>> b = 3
>>> round(a*1.0 / b,2)

0.67000000000000004

Inspite of specifying 2 in 2nd attribute of round, it outputs all the
digits after decimal.

Girish Sahani, Jun 20, 2006

2. ### Sybren StuvelGuest

Girish Sahani enlightened us with:
> I want to truncate every number to 2 digits after the decimal point. I
> tried the following but it doesnt work.

Yes it does, read the documentation about floating points.

>>>> a = 2
>>>> b = 3
>>>> round(a*1.0 / b,2)

> 0.67000000000000004

If you want to format it, use '%.2f' % (float(a)/b)

Sybren
--
The problem with the world is stupidity. Not saying there should be a
capital punishment for stupidity, but why don't we just take the
safety labels off of everything and let the problem solve itself?
Frank Zappa

Sybren Stuvel, Jun 20, 2006

3. ### MTDGuest

> >>> a = 2
> >>> b = 3
> >>> round(a*1.0 / b,2)

> 0.67000000000000004
>
> Inspite of specifying 2 in 2nd attribute of round, it outputs all the
> digits after decimal.

This is because of floating point inaccuracy. The system cannot
accurately represent some integers, however it does its best to
approximate them. Notice this:

>>> x = 2.0/3
>>> x

0.66666666666666663
>>> round(x,2)

0.67000000000000004
>>> s = str(round(x,2))
>>> s

'0.67'

MTD, Jun 20, 2006
4. ### MTDGuest

> The system cannot
> accurately represent some integers,

Er, I meant FLOATS. Doh.

Anyway, just to underline the example:

>>> x

0.66666666666666663
>>> s = str(round(x,2))
>>> s

'0.67'
>>> f = float(s)
>>> f

0.67000000000000004
>>> f == round(x,2)

True

MTD, Jun 20, 2006
5. ### Laurent PointalGuest

Girish Sahani a écrit :
> Hi,
>
> I want to truncate every number to 2 digits after the decimal point. I
> tried the following but it doesnt work.
>
>>>> a = 2
>>>> b = 3
>>>> round(a*1.0 / b,2)

> 0.67000000000000004
>
> Inspite of specifying 2 in 2nd attribute of round, it outputs all the
> digits after decimal.

There are two operations:

1) calculate of round(), which return a float number result, with the
well known problem of floating point numbers represantation (see the FAQ).

2) print that number, where default printing of last expression result
in the cli interpreter displays up to the highest precision, print
statement works differently:

>>> a=2
>>> b=3
>>> c=round(a*1.0/b,2)
>>> c

0.67000000000000004
>>> print c

0.67
>>>

A+

Laurent.

Laurent Pointal, Jun 20, 2006
6. ### Scott David DanielsGuest

Sybren Stuvel wrote:
> Girish Sahani enlightened us with:
>> I want to truncate every number to 2 digits after the decimal point....
>>>>> a = 2
>>>>> b = 3
>>>>> round(a*1.0 / b,2)

>> 0.67000000000000004

>
> If you want to format it, use '%.2f' % (float(a)/b)

Sybren has this right. If you follow everyone else's advice,
you'll eventually discover:

>>> print round(11024. / 5000.1, 2)

only gives you "2.2", not "2.20" (which is what, I suspect, you want).

--Scott David Daniels

Scott David Daniels, Jun 20, 2006
7. ### Dan BishopGuest

MTD wrote:
> > The system cannot
> > accurately represent some integers,

>
> Er, I meant FLOATS. Doh.

You were also right the first time. But it only applies to integers
with more than 53 bits.

Dan Bishop, Jun 20, 2006
8. ### AahzGuest

In article <>,
Girish Sahani <> wrote:
>
>I want to truncate every number to 2 digits after the decimal point. I
>tried the following but it doesnt work.
>
>>>> a = 2
>>>> b = 3
>>>> round(a*1.0 / b,2)

>0.67000000000000004
>
>Inspite of specifying 2 in 2nd attribute of round, it outputs all the
>digits after decimal.

You should also consider switching to the decimal module if you care
about getting correct results.
--
Aahz () <*> http://www.pythoncraft.com/

"I saw `cout' being shifted "Hello world" times to the left and stopped
right there." --Steve Gonedes

Aahz, Jun 20, 2006
9. ### per9000Guest

Hi,

just a thought: if you *always* work with "floats" with two decimals,
you are in fact working with integers, but you represent them as a
floats - confusing for the internal representation.

So why not work with int(float * 100) instead? This way you only have
to take care of roundoffs etc when dividing.

"int (+|-|*) int" = int
"int / int" = int / int + int % int

Integers are nice, me like integers.

/per9000

per9000, Jun 21, 2006
10. ### per9000Guest

oops, should be something like this:

"int / int" = "int / int, int % int"

/per9000

per9000, Jun 21, 2006
11. ### jean-michel bain-cornuGuest

> just a thought: if you *always* work with "floats" with two decimals,
> you are in fact working with integers, but you represent them as a
> floats - confusing for the internal representation.
>
> So why not work with int(float * 100) instead? This way you only have
> to take care of roundoffs etc when dividing.

And why won't you work with decimal module ?

jean-michel bain-cornu, Jun 21, 2006
12. ### Nick MaclarenGuest

In article <>,
"per9000" <> writes:
|>
|> just a thought: if you *always* work with "floats" with two decimals,
|> you are in fact working with integers, but you represent them as a
|> floats - confusing for the internal representation.

No, you aren't - you are working with fixed-point, which is something
that is neither integers nor floating-point, but is somewhere in
between. I am (just) old enough to remember when it was used for
numeric work, and to have used it for that myself, but not old enough
to have done any numeric work using fixed-point hardware.

|> So why not work with int(float * 100) instead? This way you only have
|> to take care of roundoffs etc when dividing.

And multiplying, and calling most mathematical functions.

Regards,
Nick Maclaren.

Nick Maclaren, Jun 21, 2006
13. ### per9000Guest

Nick Maclaren wrote:
> |> just a thought: if you *always* work with "floats" with two decimals,
> |> you are in fact working with integers, but you represent them as a
> |> floats - confusing for the internal representation.
>
> No, you aren't - you are working with fixed-point

Nick, your answer has so many layers, I'll try to explain how I think
:-D

1) if you use integers you can think of them as having one part bigger
than 100 and one part smaller than 100, like so:
>>> a = 11122
>>> (a/100,a%100)

(111, 22)
Here the output 111,22 looks like something else than an integer, but
this is just a matter of representation. a *is* an integer, but we
represent it *as if it was* a "decimal" number. (Compare with
(minutes,seconds) or (euro,cents) or (feet,inch) or any other
"arbitrary" position system)

2) If we use floats with two decimals
>>> b = 222.33
>>> b

222.33000000000001
they look like fix-point numbers (I had to look it up
http://en.wikipedia.org/wiki/Fixed-point :-D) but python stores it
(correct me if I am wrong) as a float (or double or quad or whatever).
If we want to work with fix-point aritmetics we have to invent new
functions to do most math.

3) Most "decimal numbers" cannot be stored exactly as floats - that is
why b gave the ugly print. But some can, f.x
>>> quart = 0.25
>>> quart

0.25
quart translates to a finite "decimal" number in binary (0.01 I think).

The point is: representing should-be integers as floats makes you loose
precision (negligable probalby but still...).

4)
> |> So why not work with int(float * 100) instead? This way you only have
> |> to take care of roundoffs etc when dividing.
>
> And multiplying, and calling most mathematical functions.

You are correct of course. My mistake.

But, the multiplication is exact before you start rounding off - I wont
start counting ordos for int*int vs. float*float, but it could have
>>> a

11122
>>> b

22233
>>> a*b

247275426
>>> (a*b/10000,a*b%10000)

(24727, 5426)
On the other hand you will quickly loose accuracy if you perform
multiple multiplications or divisions or use other mathematical
functions.

5) So, when could this way of thinking be useful? Well, rarely, but if
you only add/subtract "decimals" and/or multiply "decimals" with whole
numbers or if you want to use some non-metric system to do scientific
stuff (compute square feet when having (feet1,inch1) * (feet2,inch2)
assuming that inches are atomic.)

This could of course be extended to
(feet, inch, quarter_of_afoot, sixteeth_of_a_foot) if you'd like - it
is all a matter of representation.

Regards,
Per
----
"It is a gift. A gift to the foes of 'the Terrorists'. Why not
use this 'terrorism'? Long has my father, 'George Bush Sr',
kept the forces of 'the terrorists' at bay. By the blood of
our people are your lands kept safe. Give 'the land of the
brave' the weapon of the enemy. Let us use it against him."

per9000, Jun 21, 2006
14. ### Scott David DanielsGuest

Nick Maclaren wrote: (of fixed point)
> .... I am (just) old enough to remember when it was used for
> numeric work, and to have used it for that myself, but not old enough
> to have done any numeric work using fixed-point hardware.

You are using fixed point hardware today. Fixed point tracked the
"decimal point" (or "binary point" or whatever) in the mind of the
programmer, not in the state of the hardware. There never was
"fixed point hardware," it was simply a way of viewing the results
of the gates of the same hardware we use today.

--
--Scott David Daniels

Scott David Daniels, Jun 21, 2006
15. ### Nick MaclarenGuest

In article <44997ea8\$>,
Scott David Daniels <> writes:
|> Nick Maclaren wrote: (of fixed point)
|> > .... I am (just) old enough to remember when it was used for
|> > numeric work, and to have used it for that myself, but not old enough
|> > to have done any numeric work using fixed-point hardware.
|>
|> You are using fixed point hardware today. Fixed point tracked the
|> "decimal point" (or "binary point" or whatever) in the mind of the
|> programmer, not in the state of the hardware. There never was
|> "fixed point hardware," it was simply a way of viewing the results
|> of the gates of the same hardware we use today.

Er, no. Analogue hardware never was fixed-point, and I have used that

More relevantly, you are using a very parochial and unusual interpretation
of the word 'hardware'. In normal usage, it includes everything below
the instruct set specification (now often called the ABI). And I can
assure you that there is a considerable difference between the hardware
that provides a floating-point interface at the ABI and that which
provides a fixed-point interface.

Regards,
Nick Maclaren.

Nick Maclaren, Jun 21, 2006
16. ### rasonage

Joined:
Dec 17, 2011
Messages:
1
similar problem

floatVal = .4350001
"%.2f" % floatVal

To get .43 works great, but what if I wanted to have the decimal of what I truncate to be of variable input?
it's not like it would work this way:

accuracy = 2
floatVal = .4350001

"%.%if" %(floatVal, min_accuracy)

I'm trying to get the pointer "accuracy" as a value that can be changed/entered via user input so users can change what decimal place to round to. How would I do that?

rasonage, Dec 17, 2011