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Base 10

Base 10. 2 3 4 5 6 7 8 9 10. Powers of 10 . Alt 1 More videos and other sources on powers of 10. big numbers. Large numbers: it's the law.

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Base 10

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  1. Base 10 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10

  2. Powers of 10 • Alt 1 • More videos and other sources on powers of 10

  3. big numbers

  4. Large numbers: it's the law • Given a random variable with a finite expected value, if its values are repeatedly sampled, as the number of these observations increases, their mean will tend to approach and stay close to the expected value.

  5. These are a few of my least favorite things

  6. Viruses vary in shape from simple helical and icosahedral shapes, to more complex structures. They are about 100 times smaller than bacteria • Bacterial cells are about one tenth the size of eukaryotic cells and are typically 0.5–5.0 micrometres in length • There are approximately five nonillion (5×10^30) bacteria on Earth, forming much of the world's biomass.

  7. YouTube - From Quarks to Outer Space • Quark: 100 attometers • Milky way: 100,000 light years

  8. Orders of Magnitude • Shannon number • the number of atoms in the observable Universe is estimated to be between 4x10^79 and 10^81.

  9. How big is a googol? • Numbers have names

  10. Some small numbers • 10 trillion: national debt • 1 trillion: a partial bailout • 300 million: number of americans • 1 billion: 3 x (number of americans) (approx) • 1 trillion: 1000 x 1 billion • $ 30,000: your share of the national debt

  11. Visualizing quantities • How many pennies would it take to fill the empire state building?

  12. How to make bigger numbers faster • There is no biggest number • N+1 > N • 2*N>N • N^2>N if N>1 • Googol: 10^100 • Googolplex: 10^googol • “10^big = very big”

  13. Power towers

  14. Power towers and large numbers

  15. Large prime numbers • Euclid: there are infinitely many prime numbers • Proof: given a list of prime numbers, multiply all of them together and add one. • Either the new number is prime or there is a smaller prime not in the list.

  16. Euclid’s algorithms: GCD • The greatest common divisor of M and N is the largest whole number that divides evenly into both M and N • GCD (6 , 15 ) = 3 • If GCD (M, N) = 1 then M and N are called relatively prime. • Euclid’s algorithm is a method to find GCD (M,N)

  17. Euclid’s algorithm • M and N whole numbers. • Suppose M<N. If N is divisible by M then GCD(M,N) = M • Otherwise, subtract from N the biggest multiple of M that is smaller than N. Call the remainder R. • Claim: GCD(M,N) = GCD (M,R). • Repeat until R divides into previous.

  18. Example: GCD (105, 77) • 49 does not divide 105. • Subtract 1*77 from 105. Get R=28 • 28 does not divide into 77. Subtract 2*28 from 77. Get R=77-56=21 • Subtract 21 from 28. Get 7. • 7 divides into 21. Done. • GCD (105, 77) = 7.

  19. Exercise: find GCD (1234,121)

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