# Author Carlos Neves Carlos Neves, lemburg, mark.dickinson, rhettinger, stutzbach 2020-07-02.20:06:25 -1.0 Yes <1593720386.55.0.143813033698.issue41198@roundup.psfhosted.org>
Content
```Hi,

I am observing unexpected behavior with round built-in function about (1) significant figures in analytical methods and (2) number of odd and even numbers obtained by this function.

https://docs.python.org/3/library/functions.html#round

https://en.wikipedia.org/wiki/Significant_figures

1. Significant Figures
======================

For example, when I say 1.20 in analytical methods, I am confident about the last digit, the zero. It has a meaning. But, when I use Python,

>>> round (1.203, 2)
1.2
>>>

the zero not appears. It is not occur when the second digit is not zero.

>>> round (1.213, 2)
1.21
>>>

The zero should be printed like the other numbers to be consistent with the significant figures. Maybe other functions could present the same behavior.

2. Rounding procedure
=====================

I wrote the following code to test the number of odd and even numbers during a round procedure. I should get half-and-a-half of odd and even numbers. But the result using the round function is different. We observed 5 even more and 5 odd less. This behavior causes a systematic error.

https://en.wikipedia.org/wiki/Rounding

I hope to be contributing to the improvement of the code.

######################################################
# This code count the number of odd and even number with different procedures: truncate, round simple and round function
# Test condition: Rounding with one digit after the decimal point.

import numpy as np

even_0 = 0
odd_0 = 0

even_1 = 0
odd_1 = 0

even_2 = 0
odd_2 = 0

even_3 = 0
odd_3 = 0

# generate 1000 numbers from 0.000 up to 1 with step of 0.001
x = np.arange(0,1,0.001)

# printing
for i in range(len(x)):

x_truncated = int((x[i]*10)+0.0)/10 # no rounding
x_rounded_simple = int((x[i]*10)+0.5)/10 # rounding up at 5
x_rounded_function = round(x[i],1) # rounding by function with one digit after the decimal point

# counting odd and even numbers
if int(x[i]*1000) % 2 == 0:
even_0 += 1
else:
odd_0 += 1

if int(x_truncated*10) % 2 == 0:
even_1 += 1
else:
odd_1 += 1

if int(x_rounded_simple*10) % 2 == 0:
even_2 += 1
else:
odd_2 += 1

if int(x_rounded_function*10) % 2 == 0:
even_3 += 1
else:
odd_3 += 1

print ("{0:.3f} {1:.1f} {2:.1f} {3:.1f}".format((x[i]), x_truncated, x_rounded_simple, x_rounded_function))

print ("Result:")
print ("Raw: Even={0}, Odd={1}".format(even_0,odd_0))
print ("Truncated: Even={0}, Odd={1}".format(even_1,odd_1))
print ("Rounded simple: Even={0}, Odd={1}".format(even_2,odd_2))
print ("Rounded Function: Even={0}, Odd={1}".format(even_3,odd_3))

######################################################

Output
...
0.995 0.9 1.0 1.0
0.996 0.9 1.0 1.0
0.997 0.9 1.0 1.0
0.998 0.9 1.0 1.0
0.999 0.9 1.0 1.0
Result:
Raw: Even=500, Odd=500
Truncated: Even=500, Odd=500
Rounded simple: Even=500, Odd=500
Rounded Function: Even=505, Odd=495

----```
History
Date User Action Args
2020-07-02 20:06:26Carlos Nevessetrecipients: + Carlos Neves, lemburg, rhettinger, mark.dickinson, stutzbach
2020-07-02 20:06:26Carlos Nevessetmessageid: <1593720386.55.0.143813033698.issue41198@roundup.psfhosted.org>