mathslover
  • mathslover
I wanna know some basic applications of "Number System" and some interesting facts or interesting theory?
Mathematics
katieb
  • katieb
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mathslover
  • mathslover
Number system may include: 1) Natural Numbers 2) Whole Numbers 3) Rationalizing 4) Integers 5) Fractions, Rational Numbers 6) Irrational Numbers 7) Imaginary Numbers
mathslover
  • mathslover
if any1 know something other then this all then is welcomed to tell... @asnaseer @mukushla @waterineyes @satellite73
mathslover
  • mathslover
like rationalizing factor? also are there any uses of these all in our daily life?

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mathslover
  • mathslover
@heisenberg
King
  • King
there are interesting problems and formulas like , find the unit digit of 3^x 2^x and so on....
mathslover
  • mathslover
for example?
King
  • King
rational numbers are used in banks..
mathslover
  • mathslover
@myininaya and @UnkleRhaukus may also want to share their knowledge here
King
  • King
eg.3^20 now see 1st 4 powers of 3 3^1=3 3^2=9 3^3=27 3^4=81 unit digits are 3,9,7,1 and after this the same pattern will be repeated.. now divide 1/4=remainder is 1 so, for remainder: 1 unit digit is 3 2 unit digit is 9 3 unit digit is 7 0 unit digit is 1 so divide 20/4 remainder is 0 so unit digit of 3^20 is 1
mathslover
  • mathslover
what about 4^56 ?
mathslover
  • mathslover
find the unit digit of 4^{56} /
King
  • King
uhh...4
King
  • King
fr 4 its 4,6,4,6
King
  • King
oh sry itz 6!
mathslover
  • mathslover
right is it necessary to have 4 chances ? I mean that in 3 we took : 3 , 9 , 7 and 1 in 4 we took 4
mathslover
  • mathslover
similarly for 7 we will take: 7 , 9 , 3, 1
mathslover
  • mathslover
right?
King
  • King
yeah!
mathslover
  • mathslover
So i have: 7^{256} unit number as : 1
King
  • King
yeah.....
King
  • King
7^226 unit digit is 9
mathslover
  • mathslover
226/4 = remainder = 2 that is we have 9
King
  • King
yeah...
mathslover
  • mathslover
hmn thanks any more concept you know?
mathslover
  • mathslover
Like rationalizing factor? and magic square?
King
  • King
magic square is a square in which the sum of numbers in horizontal,vertical and diagonal way is the same...it is sriously tough to create one...
mathslover
  • mathslover
1 2 3 3 4 5 x y z 1 + 3 + x = 2+4+y = 3+5+z x + 4 + 3 = z + 4 + 1 1+2+3 = 3+4+5 m wrong :P well yes it is seriously tough and it involves gr8 thinking
mathslover
  • mathslover
You know rationalizing factor?
King
  • King
ok see rationalizing factor is like suppose u have 1/sqrt3+2 now if u multiply sqrt3 +2 by sqrt 3-2 u will get a rational number so sqrt3 -2 is the rationalizing factor of sqrt3+2...understand?
mathslover
  • mathslover
\[\large{\frac{1}{\sqrt{3}+2}}\] \[\large{\frac{\sqrt{3}-2}{1}}\] Oh k so we have rationalizing factor = \(\sqrt{3}-2\)
mathslover
  • mathslover
for example I have : \[\large{\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}}\] so the rationalizing factor is \(\frac{\sqrt{2}}{2}\)
King
  • King
yeah...
King
  • King
no fr 1st one yeah fr 2nd one sqrt 2 rationalizing factor is sqrt2 bcuz sqrt 2*sqrt2=2
mathslover
  • mathslover
oh right so we have rationalizing factor as : 2 - \sqrt{3} ?
King
  • King
@mathslover http://openstudy.com/study#/updates/503b9296e4b007f90030f59c go on this link and check this guy out..he is hmmm..
mathslover
  • mathslover
wait asnaseer is here... if he can't do anything I will interrrupt there
King
  • King
no fr 1st one i.e fr \[\frac{1}{\sqrt{3}+2}\] sqrt 3 +2 is rationalized that is it becomes a rational number when multiplied with a certain number that certain number is the rationalizing factor in this case its sqrt3-2
King
  • King
u understood? @mathslover
mathslover
  • mathslover
oh k I got it now.
mathslover
  • mathslover
yes thanks a lot @King thanks "dost"
King
  • King
k bye gtg now...ure welcome...ure indian?
mathslover
  • mathslover
yes

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