  Limiting floats to two decimal points

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I want a to be rounded to 13.95.

>>> a
13.949999999999999
>>> round(a, 2)
13.949999999999999

The round function does not work the way I expected.

You are running into the old problem with floating point numbers that not all numbers can be represented exactly. The command line is just showing you the full floating point form from memory.

With floating point representation, your rounded version is the same number. Since computers are binary, they store floating point numbers as an integer and then divide it by a power of two so 13.95 will be represented in a similar fashion to 125650429603636838/(2**53).

Double precision numbers have 53 bits (16 digits) of precision and regular floats have 24 bits (8 digits) of precision. The floating point type in Python uses double precision to store the values.

For example,

>>> 125650429603636838/(2**53)
13.949999999999999

>>> 234042163/(2**24)
13.949999988079071

>>> a = 13.946
>>> print(a)
13.946
>>> print("%.2f" % a)
13.95
>>> round(a,2)
13.949999999999999
>>> print("%.2f" % round(a, 2))
13.95
>>> print("{:.2f}".format(a))
13.95
>>> print("{:.2f}".format(round(a, 2)))
13.95
>>> print("{:.15f}".format(round(a, 2)))
13.949999999999999

If you are after only two decimal places (to display a currency value, for example), then you have a couple of better choices:

1. Use integers and store values in cents, not dollars and then divide by 100 to convert to dollars.
2. Or use a fixed point number like decimal.

There are new format specifications, String Format Specification Mini-Language:

You can do the same as:

"{:.2f}".format(13.949999999999999)

Note 1: the above returns a string. In order to get as float, simply wrap with float(...):

float("{:.2f}".format(13.949999999999999))

Note 2: wrapping with float() doesn"t change anything:

>>> x = 13.949999999999999999
>>> x
13.95
>>> g = float("{:.2f}".format(x))
>>> g
13.95
>>> x == g
True
>>> h = round(x, 2)
>>> h
13.95
>>> x == h
True

The built-in round() works just fine in Python 2.7 or later.

Example:

>>> round(14.22222223, 2)
14.22

Check out the documentation.

I feel that the simplest approach is to use the format() function.

For example:

a = 13.949999999999999
format(a, ".2f")

13.95

This produces a float number as a string rounded to two decimal points.

Nobody here seems to have mentioned it yet, so let me give an example in Python 3.6"s f-string/template-string format, which I think is beautifully neat:

>>> f"{a:.2f}"

It works well with longer examples too, with operators and not needing parens:

>>> print(f"Completed in {time.time() - start:.2f}s")

Use

print"{:.2f}".format(a)

print"{0:.2f}".format(a)

Because the latter may lead to output errors when trying to output multiple variables (see comments).

TLDR ;)

The rounding problem of input / output has been solved definitively by Python 2.7.0 and 3.1.

A correctly rounded number can be reversibly converted back and forth:
str -> float() -> repr() -> float() ... or Decimal -> float -> str -> Decimal
A Decimal type is not necessary for storage anymore.

(Naturally, it can be necessary to round a result of addition or subtraction of rounded numbers to eliminate the accumulated last bit errors. An explicit Decimal arithmetic can be still handy, but a conversion to string by str() (that is with rounding to 12 valid digits) is good enough usually if no extreme accuracy or no extreme number of successive arithmetic operations is required.)

Infinite test:

import random
from decimal import Decimal
for x in iter(random.random, None):           # Verify FOREVER that rounding is fixed :-)
assert float(repr(x)) == x                # Reversible repr() conversion.
assert float(Decimal(repr(x))) == x
assert len(repr(round(x, 10))) <= 12      # Smart decimal places in repr() after round.
if x >= 0.1:                              # Implicit rounding to 12 significant digits
assert str(x) == repr(round(x, 12))   # by str() is good enough for small errors.
y = 1000 * x                             # Decimal type is excessive for shopping
assert str(y) == repr(round(y, 12 - 3))  # in a supermaket with Python 2.7+ :-)

Documentation

See the Release notes Python 2.7 - Other Language Changes the fourth paragraph:

Conversions between floating-point numbers and strings are now correctly rounded on most platforms. These conversions occur in many different places: str() on floats and complex numbers; the float and complex constructors; numeric formatting; serializing and de-serializing floats and complex numbers using the marshal, pickle and json modules; parsing of float and imaginary literals in Python code; and Decimal-to-float conversion.

Related to this, the repr() of a floating-point number x now returns a result based on the shortest decimal string that‚Äôs guaranteed to round back to x under correct rounding (with round-half-to-even rounding mode). Previously it gave a string based on rounding x to 17 decimal digits.

The related issue

More information: The formatting of float before Python 2.7 was similar to the current numpy.float64. Both types use the same 64 bit IEEE 754 double precision with 52 bit mantissa. A big difference is that np.float64.__repr__ is formatted frequently with an excessive decimal number so that no bit can be lost, but no valid IEEE 754 number exists between 13.949999999999999 and 13.950000000000001. The result is not nice and the conversion repr(float(number_as_string)) is not reversible with numpy. On the other hand: float.__repr__ is formatted so that every digit is important; the sequence is without gaps and the conversion is reversible. Simply: If you perhaps have a numpy.float64 number, convert it to normal float in order to be formatted for humans, not for numeric processors, otherwise nothing more is necessary with Python 2.7+.