## mathslover 3 years ago I wanna know some basic applications of "Number System" and some interesting facts or interesting theory?

1. 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

2. mathslover

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

3. mathslover

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

4. mathslover

@heisenberg

5. King

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

6. mathslover

for example?

7. King

rational numbers are used in banks..

8. mathslover

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

9. 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

10. mathslover

11. mathslover

find the unit digit of 4^{56} /

12. King

uhh...4

13. King

fr 4 its 4,6,4,6

14. King

oh sry itz 6!

15. 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

16. mathslover

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

17. mathslover

right?

18. King

yeah!

19. mathslover

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

20. King

yeah.....

21. King

7^226 unit digit is 9

22. mathslover

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

23. King

yeah...

24. mathslover

hmn thanks any more concept you know?

25. mathslover

Like rationalizing factor? and magic square?

26. 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...

27. 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

28. mathslover

You know rationalizing factor?

29. 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?

30. mathslover

$\large{\frac{1}{\sqrt{3}+2}}$ $\large{\frac{\sqrt{3}-2}{1}}$ Oh k so we have rationalizing factor = $$\sqrt{3}-2$$

31. mathslover

for example I have : $\large{\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}}$ so the rationalizing factor is $$\frac{\sqrt{2}}{2}$$

32. King

yeah...

33. King

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

34. mathslover

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

35. King

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

36. mathslover

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

37. 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

38. King

u understood? @mathslover

39. mathslover

oh k I got it now.

40. mathslover

yes thanks a lot @King thanks "dost"

41. King

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

42. mathslover

yes