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- What does it mean when something says (in thousands)
It means "26 million thousands" Essentially just take all those values and multiply them by 1000 1000 So roughly $26 $ 26 billion in sales
- How much zeros has the number $1000!$ at the end?
If a number ends with n n zeros than it is divisible by 10n 10 n, that is 2n5n 2 n 5 n A factorial clearly has more 2 2 s than 5 5 s in its factorization so you only need to count how many 5 5 s are there in the factorization of 1000! 1000!
- Creating arithmetic expression equal to 1000 using exactly eight 8s . . .
I would like to find all the expressions that can be created using nothing but arithmetic operators, exactly eight $8$'s, and parentheses Here are the seven solutions I've found (on the Internet)
- Look at the following infinite sequence: 1, 10, 100, 1000, 10000,
What is the proof that there are 2 numbers in this sequence that differ by a multiple of 12345678987654321?
- modular arithmetic - What is the last digit of $7^ {1000 . . .
Someone showed me this question in an linear algebra hw dealing with fields: What is the last digit of $7^{1000}$? What's the idea behind this? Thanks
- elementary number theory - How to find the last digit of $3^ {1000 . . .
The last digit of 35 3 5 is 3 3 The last digit of 36 3 6 is 9 9 Notice a pattern? Why does this pattern exist? What is going on when I multiply by three? Based on this we could guess that it has a period of 4 4 so that 34n ≡ 1 3 4 n ≡ 1 Use this to find the last digit of 31000 3 1000 (Do you know modular arithmetic? If so it is a lot easier)
- Find $A^{1000}$ by using Cayley-Hamilton Theorem
Find A1000 A 1000 by using the Cayley-Hamilton theorem I find the characteristic polynomial by P(A) = −A3 + 2A2 = 0 P (A) = A 3 + 2 A 2 = 0 (by Cayley-Hamilton) but I don't see how to find A1000 A 1000 by this characteristic polynomial
- terminology - What do you call numbers such as $100, 200, 500, 1000 . . .
There are different categories of numbers that we use every day Integers that written in decimal notation have $1, 2$ or $5$ as the leading figure, followed by none, one or more zeros These are v
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