How do you enter a repeating decimal
04-28-2021, 02:43 PM
Post: #1
 MullenJohn Junior Member Posts: 43 Joined: Sep 2017
How do you enter a repeating decimal
Help,

Using the HP Prime how does one enter a repeating decimal such as 2.(777), i.e. 2.777...777...?

Thanks - Cheers!
04-28-2021, 03:28 PM
Post: #2
 cdmackay Senior Member Posts: 665 Joined: Sep 2018
RE: How do you enter a repeating decimal
(04-28-2021 02:43 PM)MullenJohn Wrote:  Help,

Using the HP Prime how does one enter a repeating decimal such as 2.(777), i.e. 2.777...777...?

Thanks - Cheers!

2 + 7/9 ?

seriously, I don't know, but would be interested to hear.

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04-28-2021, 05:44 PM
Post: #3
 Joe Horn Senior Member Posts: 1,903 Joined: Dec 2013
RE: How do you enter a repeating decimal
(04-28-2021 03:28 PM)cdmackay Wrote:
(04-28-2021 02:43 PM)MullenJohn Wrote:  Help,

Using the HP Prime how does one enter a repeating decimal such as 2.(777), i.e. 2.777...777...?

Thanks - Cheers!

2 + 7/9 ?

seriously, I don't know, but would be interested to hear.

That's the best way. Just use as many 9's as there are repeating digits:
71.232323232323... = 71+23/99 (two 9's because there are two repeating digits)
71.234234234234... = 71+234/999 (three 9's because there are three repeating digits)

If the repeating digits do not begin immediately after the decimal point, then ALSO insert as many zeros after the 9's as there are non-repeating digits after the decimal point:
71.2344444444444... = 71.23 + 4/900
(One 9 because one digit is repeating; two 0's because two digits after the decimal point don't repeat)
71.2345656565656... = 71.234 + 56/99000
(two 9's because two digits repeat; three 0's because three digits after the decimal point don't repeat)

This is especially useful in CAS where the above yield exact results. In Home, it's often more efficient to simply key in the decimal approximation, since Home view is intended for approximate math anyway.

<0|ɸ|0>
-Joe-
04-29-2021, 11:07 AM
Post: #4
 jonmoore Member Posts: 224 Joined: Apr 2020
RE: How do you enter a repeating decimal
(04-28-2021 05:44 PM)Joe Horn Wrote:  This is especially useful in CAS where the above yield exact results. In Home, it's often more efficient to simply key in the decimal approximation, since Home view is intended for approximate math anyway.

Great tips Joe.

But this reminds me of a bugbear with the prime. The only way to change an improper fraction result to a mixed fraction in the CAS view is to use the propFrac function. The a b/c key only works with fractions in the Home view, where more often than not, you're working with approximate decimal values.

I'm not sure if my memory is playing tricks on me, but I could swear it wasn't always this way.
04-29-2021, 01:07 PM (This post was last modified: 04-29-2021 01:13 PM by Albert Chan.)
Post: #5
 Albert Chan Senior Member Posts: 2,109 Joined: Jul 2018
RE: How do you enter a repeating decimal
I had coded repeating decimal conversion in Python, long time ago.
Code:
def dratio(s):     'Return decimals (with no exponent) as ratio'     s = s.rstrip(') \t')     i = s.find('.')     if i < 0: return int(s), 1  # assume integer, if no decimal point     j = s.find('(', i+1)        # repeating decimal start     if j < 0: return int(s[:i]+s[i+1:]), 10 ** (len(s)-i-1)     r = 10 ** (len(s)-j-1)      # handle repeating decimals     k = int( s[:i] + s[i+1:j] + s[j+1:] )     return k - k//r - (k<0), (r-1) * 10 ** (j-i-1)

>>> map(dratio, ['2.(777)', '71.23(4)', '71.234(56)'])
[(2775, 999), (64111, 900), (7052222, 99000)]
>>> [n/d for (n,d) in _]
[2.7777777777777777, 71.234444444444449, 71.23456565656565]

Code get the correct ratio, but not fully reduced. Fix is easy, if needed.

>>> import fractions
>>> dtoF = lambda s: fractions.Fraction(*dratio(s))
>>> map(dtoF, ['2.(777)', '71.23(4)', '71.234(56'])
[Fraction(25, 9), Fraction(64111, 900), Fraction(3526111, 49500)]
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