Math Is Fun Forum / 10 second questions

mathsyperson · 2006-09-29 02:55:53

It's only a problem if you have a number or algebraic expression at the end of your sentence though. It's fine to be emotional as long as you use strategic sentence structure.

"And now by reducing the fraction, we can see that the equation is solved!"

You could also possibly get around it by saying "And now we see that the answer is two!" or similar, depending on how strict the teacher is. I've never seen factorials applied to numbers as words.

Although technically, if the answer was 2 then saying 2! wouldn't even be wrong.

ganesh · 2006-09-29 14:13:41

18. If 1000 kilobytes is a megabyte,
1000 megabytes a gigabyte, what is 1000 gigabytes?

19. What would be the last digit of 6^100?

20. Is 1001 a prime number?

Devantè · 2006-09-29 16:14:58

18. 1 Terabyte
19. I'll come back to later
20. No

luca-deltodesco · 2006-09-29 16:39:04

19. 6

Devantè · 2006-09-29 17:03:43

Oops, didn't realise 6^n (n not being 0 or 1) would always end in a 6.

ganesh · 2006-09-29 22:17:10

Excellent, devante` and luca-deltodesco!!!
To devante` : Any power of a number ending in 0,1,5,6 always end in 0,1,5,6 respectively.

21. Is 133 a prime number?

22. How many squares are there from 1 to 1000, inculding 1?

23. And how many cubes?

ganesh · 2006-09-29 22:30:19

24. Whats special about the number 0.4771................?

25. How many cubes, including 1, are there from 1 to 1000?

Devantè · 2006-09-30 01:51:15

21. No
22. Hmm...31?
23. 10
24. The mark for 3 is located about 0.4771 units from the mark for 1 (to do with Slide Rules)
25. Haven't you already asked that question? Anyway, 10.

Oh, and thanks Ganesh for that.

I wasn't taught that rule.

Last edited by Devanté (2006-09-30 01:51:41)

ganesh · 2006-10-03 15:27:55

26. What is 6 x 6 x 6?

27. Is 343 a prime number?

mathsyperson · 2006-10-03 23:47:44

26. 216

27. No. If you take the last digit of 343 and multiply it by 2, then take that away from the rest of 343, you get 34 - (2*3) = 28. 28 is divisible by 7, which means that 343 also is.

...OK, I just wanted to show off that cool method that I know of finding multiples of 7 that probably takes longer than just dividing the number by 7 anyway. But I recognised that 343 was 7³, so I still did it in under 10 seconds.

ganesh · 2006-10-04 01:39:40

Excellent, mathsyperson!
Knowing 343 is 7^3 is remarkable!!!

28. What is 6!?

29. Aprroximately how many kilometers is a light year?

30. What is sin45+cos45 (degrees)?

espeon · 2006-10-04 01:43:06

u know 28 what does the !?mean?

ganesh · 2006-10-04 01:47:34

! means factorial.
1! is 1.
2! is 2x1=2.
3!=3x2x1=6.
4!=4x3x2x1=24
5!=5x4x3x2x1=120.

Factorials are very important in combinatorics. Like finding permuations and combinations. espeon, you would soon be taught in school about permutations and combinations in probability. You can refer our formuls section for getting the formulas.

espeon · 2006-10-04 01:55:58

so ! means everything upto it so 6! is

6x5x4x3x2x1=720?

ganesh · 2006-10-04 02:01:01

Very well done, espeon! You are correct!
7! is 7x6x5x4x3x2x1=5040
9! is 9x8x7x6x5x4x3x2x1 = 362880
10! is 10x9x8x7x6x5x4x3x2x1=3628800
100! contains about 160 digits and so on.

espeon · 2006-10-04 02:21:22

lol yay!

mathsyperson · 2006-10-04 03:39:52

29. 3*10^5 * 3600 *24 * 365 ≈ 10^13 km

30. sin45 + cos45 = 1/√2 + 1/√2 = 2/√2 = 2√2/2 = √2

Devantè · 2006-10-04 06:05:21

26. 216
27. Nope
28. 720
29. 1 light year = 9.4605284 × 10^12 km (simplified)
30. √2, depending on the form you want it in

Mathsyperson did it before me.

Devantè · 2006-10-04 06:10:24

Oops, 29 should be:

1 kilometer = 1.05702341 × 10^-13 light years

ganesh · 2006-10-04 14:17:04

Very well done, mathsyperson and Devante`.
Devante, the answer to #29 should be 10^13 kilometers, not 10^-13 kilometers. Also, 1 light year 10^13 kilometers, not the other way round.

Devantè · 2006-10-04 16:42:18

OK, thanks for that. I always get muddled with light year conversion.

ganesh · 2006-10-05 01:29:38

Devante`, a light year is 365x86140x3x10^8 approximately.

And a parsec is about 3.26 light years. A kiloparsec is 1,000 parsecs.

I am giving this information because all mathematicians are exepected to be very good in Astronomy.

31. How many kilometers is a mile approximately?

32. How many pounds is a kilogram approximately?

Devantè · 2006-10-05 01:43:11

31. 1 mile = 1.609344 kilometers
32. 1 kilogram = 2.20462262 pounds

ganesh · 2006-10-05 01:46:51

Devante`,
You are correct. Very well done.

ganesh · 2006-10-05 01:48:19

33. How many zeros does a quintillion (US) contain?

34. What is special about the number 26?

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#26 2006-09-29 02:55:53

Re: 10 second questions

#27 2006-09-29 14:13:41

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#28 2006-09-29 16:14:58

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#29 2006-09-29 16:39:04

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#30 2006-09-29 17:03:43

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#31 2006-09-29 22:17:10

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#32 2006-09-29 22:30:19

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#33 2006-09-30 01:51:15

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#35 2006-10-03 23:47:44

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#36 2006-10-04 01:39:40

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#39 2006-10-04 01:55:58

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#42 2006-10-04 03:39:52

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