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Dec 13th, 2008

Rounding to n digits

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Hi again i have programmed a thing that asks for 2 numbers and does a series of things to it.But i want to round the square-rooted numbers to about 6 digits e.g. 5.12345. How can this be done?

Here is my code:

(Toggle Plain Text)

from math import sqrt
running = 'Y'

while 'Y' in running or 'y' in running:
    #defining numbers
    startn = float(raw_input('What is the starting number'))
    startn2 = startn
    endn = float(raw_input('What is the ending number?'))
    endn2 = endn
    #defining lists
    num = []
    nums = []
    numsq = []
    while startn2 != (endn2+1):
        #just the numbers
        a = int(startn2)
        num.append(a)
        startn2+=1
    startn2 = startn
    print 'numbers without changing are:', num
    while startn2 != (endn2+1):
        #numbers squared
        a = int(startn2*startn2)
        nums.append(a)
        startn2+=1
    startn2 = startn
    print 'numbers squared are:', nums
    while startn2 != (endn2+1):
        #numbers square-rooted
        #Here is my problem, i want to simplify it to about 6 digits e.g. 5.12345
        a = sqrt(startn2)
        numsq.append(a)
        startn2+=1
    startn2 = startn
    print 'numbers square-rooted are:', numsq
    running = raw_input('Try another set? (Y or N)')

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leegeorg07

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Dec 13th, 2008

Re: Rounding to n digits

>But i want to round the square-rooted numbers to about 6 digits e.g. 5.12345. How can this be done?

Take a look at round()

Aia

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Dec 13th, 2008

Re: Rounding to n digits

Built-in function round() and string formatting.

Python Syntax (Toggle Plain Text)
>>> round(math.pi, 5)
3.1415899999999999
>>> "%0.5f" % math.pi
'3.14159'
>>> sig_digits = 6
>>> num = 123.456789
>>> "%0.*f" % (sig_digits-len(str(num).split('.')[0]), num)
'123.457'
>>> num = 1.23456789
>>> "%0.*f" % (sig_digits-len(str(num).split('.')[0]), num)
'1.23457'
>>> num = 1234567890
>>> "%0.*f" % (sig_digits-len(str(num).split('.')[0]), num)
'1234567890'
>>>
>>> round(math.pi, 5)
3.1415899999999999
>>> "%0.5f" % math.pi
'3.14159'
>>> sig_digits = 6
>>> num = 123.456789
>>> "%0.*f" % (sig_digits-len(str(num).split('.')[0]), num)
'123.457'
>>> num = 1.23456789
>>> "%0.*f" % (sig_digits-len(str(num).split('.')[0]), num)
'1.23457'
>>> num = 1234567890
>>> "%0.*f" % (sig_digits-len(str(num).split('.')[0]), num)
'1234567890'
>>>

solsteel

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Dec 14th, 2008

Re: Rounding to n digits

To represent a floating point number in a formatted form for print, you have to store the result as a string in your list:

python Syntax (Toggle Plain Text)
# representing print formatted floats in a list
 
list_floats = [1/3.0, 1/6.0, 3.124567, 5.01]
 
print list_floats
 
"""
my output (note the typical float representation problem) -->
[0.33333333333333331, 0.16666666666666666, 3.1245669999999999, 5.0099999999999998]
"""
 
# create a new list of floats using round()
list_floats2 = []
for n in list_floats:
    list_floats2.append(round(n, 5))
 
print list_floats2
 
"""
my output (notice we are still dealing with floats) -->
[0.33333000000000002, 0.16667000000000001, 3.1245699999999998, 5.0099999999999998]
"""
 
# to make round() stick for your print
# you have to store the result as a string
list_floats3 = []
for n in list_floats:
    list_floats3.append(str(round(n, 5)))
 
print list_floats3
 
"""
my output -->
['0.33333', '0.16667', '3.12457', '5.01']
"""
 
# or ...
list_floats4 = []
for n in list_floats:
    list_floats4.append("%0.5f" % n)
 
print list_floats4
 
"""
my output -->
['0.33333', '0.16667', '3.12457', '5.01000']
"""
# representing print formatted floats in a list

list_floats = [1/3.0, 1/6.0, 3.124567, 5.01]

print list_floats

"""
my output (note the typical float representation problem) -->
[0.33333333333333331, 0.16666666666666666, 3.1245669999999999, 5.0099999999999998]
"""

# create a new list of floats using round()
list_floats2 = []
for n in list_floats:
    list_floats2.append(round(n, 5))

print list_floats2

"""
my output (notice we are still dealing with floats) -->
[0.33333000000000002, 0.16667000000000001, 3.1245699999999998, 5.0099999999999998]
"""

# to make round() stick for your print
# you have to store the result as a string
list_floats3 = []
for n in list_floats:
    list_floats3.append(str(round(n, 5)))

print list_floats3

"""
my output -->
['0.33333', '0.16667', '3.12457', '5.01']
"""

# or ...
list_floats4 = []
for n in list_floats:
    list_floats4.append("%0.5f" % n)

print list_floats4

"""
my output -->
['0.33333', '0.16667', '3.12457', '5.01000']
"""

The behaviour of a floating point number you notice here is typical of many computer languages.

Last edited by sneekula; Dec 14th, 2008 at 1:44 pm.

sneekula

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Apr 25th, 2010

Increase digits

I was trying to make a program that gives very accurate answers to problems. The accuracy I want is of like 20000 terms.
For eg. 10/3 is written as 3.33333333333333333...20,000 times.
So, is it possible in Python?
Also, please answer in reference to Python 3.0, if possible...

techie1991

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Apr 25th, 2010

Increase digits

Python Syntax (Toggle Plain Text)
import math
print(math.sqrt(2))
import math
print(math.sqrt(2))

which gives:
1.4142135623730951... which does not fulfill my need.
Also, please answer in reference to Python 3.0, if possible...

techie1991

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Apr 26th, 2010

Re: Rounding to n digits

Doing 10/3 in 20000 decimals:

Python Syntax (Toggle Plain Text)
>>> base=10**20000
>>> units,decimals = divmod(10*base/3,base) ##10/3 long number
>>> print str(units)+'.'+str(decimals)
>>> base=10**20000
>>> units,decimals = divmod(10*base/3,base) ##10/3 long number
>>> print str(units)+'.'+str(decimals)

For square root you must use own function:

Python Syntax (Toggle Plain Text)
>>> import math
>>> x=(2*base,base)
>>> math.sqrt(x[0])
 
Traceback (most recent call last):
  File "<pyshell#12>", line 1, in <module>
    math.sqrt(x[0])
OverflowError: long int too large to convert to float
>>>
>>> import math
>>> x=(2*base,base)
>>> math.sqrt(x[0])

Traceback (most recent call last):
  File "<pyshell#12>", line 1, in <module>
    math.sqrt(x[0])
OverflowError: long int too large to convert to float
>>>

Last edited by pyTony; Apr 26th, 2010 at 2:56 am.

pyTony

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Apr 26th, 2010

Re: Rounding to n digits

Start experimenting with Python module decimal ...

Python Syntax (Toggle Plain Text)
# high accuracy calculations with Python module decimal
# tested with Python 3.1.2
 
import decimal as dc
 
# regular float calculation
sqrt1 = 2 ** 0.5
 
print(type(sqrt1))
print(sqrt1)
print(sqrt1 * sqrt1)
 
# set decimal precition
dc.getcontext().prec = 60
 
# using module decimal
sqrt2 = dc.Decimal(2) ** dc.Decimal('0.5')
 
print(type(sqrt2))
print(sqrt2)
print(sqrt2 * sqrt2)
 
"""my result -->
<class 'float'>
1.41421356237
2.0
<class 'decimal.Decimal'>
1.41421356237309504880168872420969807856967187537694807317668
2.00000000000000000000000000000000000000000000000000000000000
"""
# high accuracy calculations with Python module decimal
# tested with Python 3.1.2

import decimal as dc

# regular float calculation
sqrt1 = 2 ** 0.5

print(type(sqrt1))
print(sqrt1)
print(sqrt1 * sqrt1)

# set decimal precition
dc.getcontext().prec = 60

# using module decimal
sqrt2 = dc.Decimal(2) ** dc.Decimal('0.5')

print(type(sqrt2))
print(sqrt2)
print(sqrt2 * sqrt2)

"""my result -->
<class 'float'>
1.41421356237
2.0
<class 'decimal.Decimal'>
1.41421356237309504880168872420969807856967187537694807317668
2.00000000000000000000000000000000000000000000000000000000000
"""

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