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  • elementary number theory - Sum of all the factors of $33333333 . . .
    5 What is the sum of factors of factors of $33333333$ (that's $3$ eight times)? Here's how I tried to attempt this question yet failed: Factors of $33333333=3\times11111111=3\times11\times1010101=3\times11\times101\times10001$ And now I was lost (just before the last step) as I couldn't confirm if 10001 is prime or not
  • $0. 333333$ - a recurring or non-terminating decimal?
    1) A terminating decimal representation means a number can be represented by a finite string of digits in base $10$ notation, e g $0 5$, $0 25$, $0 8$, $2 4$ 2) A non-terminating decimal representation means that your number will have an infinite number of digits to the right of the decimal point There are two sorts of non-terminating decimal numbers 2a) The first sort are called recurring
  • Finding sum of factors of a number using prime factorization
    Given a number, there is an algorithm described here to find it's sum and number of factors For example, let us take the number $1225$ : It's factors are $1, 5, 7, 25, 35, 49, 175, 245, 1225 $ and
  • Subtraction of two repeating decimals - Mathematics Stack Exchange
    Think of it this way: it's smaller than every other number The only number like this is $0$ (I'm restricting myself to talking about positives, but the basic idea is the same regardless )
  • Not clear on what we mean with numbers with infinite digits
    If you want a better approximation, say $6\cdot0 33333333=1 99999998$ instead, and so forth That answer is almost $2$, but not quite The difference is $0 00000002$ But as you add digits to $0 333\ldots$, you also get to add more nines to the answer, and you get closer and closer to $2$
  • exponentiation - If $3^ {33}+3^ {33}+3^ {33}=3^ {x}$. Solve for $x . . .
    For the last line of your answer: 3 (3³³) = 3^x Apply the exponent rules for multiplication and you get: 3¹ 3³³ = 3^x 3^ (1+33) = 3^x Then we got 1+33 = x x = 34
  • Can something be statistically impossible? - Mathematics Stack Exchange
    A statistical impossibility is a probability that is so low as to not be worthy of mentioning Sometimes it is quoted as $10^ {-50}$ although the cutoff is inherently arbitrary Although not truly impossible the probability is low enough so as to not bear mention in a rational, reasonable argument In some cases that arise in Gedanken experiments in thermodynamics, the probabilities can be
  • How many feet does 52 inches equal? - Answers
    52 inches = 4 33333333 feet To convert the dimensions of a pool from feet and inches to feet only, first convert the inches to feet Since 52 inches is equal to 52 12 = 4 33 feet, you can then add
  • Longest chain of digits in $\pi$. - Mathematics Stack Exchange
    Playing on this site, I reproduced below the longest string of repeated numbers, the position and number of times they appear in the first 200 million of digits of $\pi$ 00000000 172330850 2 11111111 159090113 3 22222222 175820910 1 33333333 36488176 1 44444444 22931745 2 55555555 168743355 1 666666666 45681781 1 777777777 24658601 1 888888888 46663520 1 99999999 66780105 1 The problem is that
  • algebra precalculus - Solving equations with multiple roots . . .
    You can eliminate roots by rearranging (square roots on the left), squaring, rearranging again (the only remaining square root on the left) and squaring again Each squaring increasing the degree of equation and introduces new "fake" solutions Solve the equation and test with the original equation each of the candidates to see which is the correct one Of course what @shubham suggests should





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