I wanna know some basic applications of "Number System" and some interesting facts or interesting theory?

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- 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

if any1 know something other then this all then is welcomed to tell...
@asnaseer @mukushla @waterineyes @satellite73

- mathslover

like rationalizing factor?
also are there any uses of these all in our daily life?

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## More answers

- mathslover

- King

there are interesting problems and formulas like ,
find the unit digit of 3^x 2^x and so on....

- mathslover

for example?

- King

rational numbers are used in banks..

- mathslover

@myininaya and @UnkleRhaukus may also want to share their knowledge here

- 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

what about 4^56 ?

- mathslover

find the unit digit of 4^{56} /

- King

uhh...4

- King

fr 4 its 4,6,4,6

- King

oh sry itz 6!

- 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

similarly for 7 we will take:
7 , 9 , 3, 1

- mathslover

right?

- King

yeah!

- mathslover

So i have:
7^{256} unit number as : 1

- King

yeah.....

- King

7^226 unit digit is 9

- mathslover

226/4 = remainder = 2 that is we have 9

- King

yeah...

- mathslover

hmn thanks any more concept you know?

- mathslover

Like rationalizing factor? and magic square?

- 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

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

You know rationalizing factor?

- 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

\[\large{\frac{1}{\sqrt{3}+2}}\]
\[\large{\frac{\sqrt{3}-2}{1}}\]
Oh k so we have rationalizing factor = \(\sqrt{3}-2\)

- mathslover

for example I have :
\[\large{\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}}\]
so the rationalizing factor is \(\frac{\sqrt{2}}{2}\)

- King

yeah...

- King

no fr 1st one yeah fr 2nd one sqrt 2 rationalizing factor is sqrt2 bcuz sqrt 2*sqrt2=2

- mathslover

oh right so we have rationalizing factor as : 2 - \sqrt{3} ?

- King

@mathslover http://openstudy.com/study#/updates/503b9296e4b007f90030f59c go on this link and check this guy out..he is hmmm..

- mathslover

wait asnaseer is here... if he can't do anything I will interrrupt there

- 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

u understood? @mathslover

- mathslover

oh k I got it now.

- mathslover

yes thanks a lot @King
thanks "dost"

- King

k bye gtg now...ure welcome...ure indian?

- mathslover

yes

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