## mathslover Group Title I wanna know some basic applications of "Number System" and some interesting facts or interesting theory? one year ago one year ago

1. mathslover Group Title

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 Group Title

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

3. mathslover Group Title

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

4. mathslover Group Title

@heisenberg

5. King Group Title

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

6. mathslover Group Title

for example?

7. King Group Title

rational numbers are used in banks..

8. mathslover Group Title

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

9. King Group Title

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 Group Title

11. mathslover Group Title

find the unit digit of 4^{56} /

12. King Group Title

uhh...4

13. King Group Title

fr 4 its 4,6,4,6

14. King Group Title

oh sry itz 6!

15. mathslover Group Title

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 Group Title

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

17. mathslover Group Title

right?

18. King Group Title

yeah!

19. mathslover Group Title

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

20. King Group Title

yeah.....

21. King Group Title

7^226 unit digit is 9

22. mathslover Group Title

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

23. King Group Title

yeah...

24. mathslover Group Title

hmn thanks any more concept you know?

25. mathslover Group Title

Like rationalizing factor? and magic square?

26. King Group Title

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 Group Title

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 Group Title

You know rationalizing factor?

29. King Group Title

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 Group Title

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

31. mathslover Group Title

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

32. King Group Title

yeah...

33. King Group Title

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

34. mathslover Group Title

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

35. King Group Title

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

36. mathslover Group Title

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

37. King Group Title

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 Group Title

u understood? @mathslover

39. mathslover Group Title

oh k I got it now.

40. mathslover Group Title

yes thanks a lot @King thanks "dost"

41. King Group Title

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

42. mathslover Group Title

yes