Since we are given numerator 'n' and denominator 'd' separately already. and
considering n and d as integers and d!=0 we can safely assume n/d as either
a terminating fraction or a non terminating but recurring fraction, in which
case we have to find the recurring digits of the fraction.
Now what I suggested was almost same as Ravi's approach.
take a Set 'S' keeping tuples (R,Q) where R is the current remainder and Q
is the factor such that d*Q is subtracted from the number to get R.
In other words. if at an intermediate step of division we have 'a' as the
divident left then Q=floor(a/d) and R=a%d
Keep dividing 'n' by 'd' like it is done manually. After every division
check-
1. If the current remainder is not present in 'S' then add current remainder
'R' and corresponding quotient 'Q' in the set
2. If R is found in the set S, then all the following entries in the set
until end will constitute the recurring digits.
taking Ravi's example:-
Example:
7) 9 (1.*285714*28 S=[]
7
--
20 S=[(2,2)]
14
---
60 S=[(2,2), (6,8)]
56
---
40 S=[(2,2), (6,8), (4,5)]
35
---
50 S=[(2,2), (6,8), (4,5),
(5,7)]
49
---
10 S=[(2,2), (6,8), (4,5),
(5,7), (1,1)]
7
----
30 S=[(2,2), (6,8), (4,5),
(5,7), (1,1), (3,4)]
28 ^
---- |
20 2 is found in S here,
so recurring digits are "285714"
14
----
60
56
repeats
hope its clear
Anurag Sharma
On Sat, Jun 12, 2010 at 4:02 PM, divya jain <sweetdivya....@gmail.com>wrote:
> @anurag
>
> i dint get ur approach..which numerator n denominator u r talking
> about..plz explain.. thanks in advance
>
> On 11 June 2010 08:57, Anurag Sharma <anuragvic...@gmail.com> wrote:
>
>> Please note that the fractional repeating part is recurring. and so that
>> 4th temporary variable assignment will be this way->
>> temp=x*10000 - x= 233456.34563456... - 23.34563456.... = 233433.0 ( mark
>> the fractional part is 0 now since the infinitely repeating 3456... will get
>> cancelled)
>> In this case you can say that 4 places are repeating. But yes its
>> according to the maths and in any programming language whenever you divide
>> the numerator and denominator you wont get this infinitely recurring decimal
>> places.
>>
>> @divya, also your approach wont work if the recurring fractional digits
>> start after few places from the decimal like in the case of
>> 23.123345634563456.... (note here after the decimal place 123 is not
>> repeating while 3456.. after this 123 is repeating.)
>>
>> What I suggest in this case is keep dividing the numerator by denominator
>> and at every step keep inserting the tupple (remainder, quotient) of that
>> division step in a set. and before inserting in the set check whether it
>> already exists. If yes then the all the quotients following from that point
>> (including the point) will be recurring.
>>
>> Regards,
>>
>> Anurag Sharma
>>
>>
>>
>> On Thu, Jun 10, 2010 at 8:25 AM, Veer Sharma
>> <thisisv...@rediffmail.com>wrote:
>>
>>> Seems it wont work...
>>> x=23.34563456
>>>
>>> temp = x*100 -x = 233.4563456 - 23.34563456 = 210.11071104
>>> temp = x*100 -x = 2334.563456 - 23.34563456 = 2311.21782144
>>> temp = x*1000 -x = 23345.63456 - 23.34563456 = 23322.28892544
>>> temp = x*10000 -x = 233456.3456 - 23.34563456 = 233432.99996544
>>> temp = x*100000 -x = 2334563.456 - 23.34563456 = 2334540.11036544
>>>
>>> ...
>>>
>>> On Jun 9, 11:24 pm, Anurag Sharma <anuragvic...@gmail.com> wrote:
>>> > multiply the original number x=23.34563456
>>> >
>>> > Anurag Sharma
>>> >
>>> > On Wed, Jun 9, 2010 at 10:36 PM, Veer Sharma <
>>> thisisv...@rediffmail.com>wrote:
>>> >
>>> >
>>> >
>>> > > One question:
>>> >
>>> > > No x = 23.34563456
>>> > > temp = x X 10 = 233.4563456
>>> > > temp = temp - x = 210.11071104
>>> > > decimal part zero? No.
>>> > > Now multiply the no. with 100. Which no? original x (= 23.34563456)
>>> or
>>> > > new no. temp (=210.11071104)?
>>> >
>>> > > On Jun 9, 8:12 pm, divya jain <sweetdivya....@gmail.com> wrote:
>>> > > > multiply the no. with 10 nd store in temp. now subtract no from
>>> temp.
>>> > > check
>>> > > > if the decimal part is zero if yes. then 1st digit after decimal
>>> is
>>> > > > recurring. if no. multiply the no with 100 and repeat . if this
>>> time
>>> > > decimal
>>> > > > part is zero then 2 digits after decimal r recurring nd so on..
>>> >
>>> > > > On 8 June 2010 21:45, Veer Sharma <thisisv...@rediffmail.com>
>>> wrote:
>>> >
>>> > > > > You have a Numerator and Denominator. After division you might
>>> get a
>>> > > > > recurring decimal points float as the answer.
>>> >
>>> > > > > Problem is: You need to identify the recurring part for a given
>>> > > > > decimal no?
>>> > > > > For example 23.34563456 ...
>>> > > > > return 3456
>>> >
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