The Uses of Large Numbers

High School Mathematics

Large numbers are used mostly used in astronomy and cosmology.  According to the Big Bang Model, the universe is estimated to be 4.3 \times 10^{17} seconds old, the observable universe is 8.8 \times 10^{26} meters, and it contains 5 \times 10^{22} stars.

In computing, if a hacker attempts to open a computer with up to a 40-character password, we should really wish him luck. Even though he may create a program that would display 1 billion strings per second indefinitely, it would take him 2 \times 10^{87} seconds or about 6 \times 10^{79} years to complete all the combinations.  That is way, way older than the universe which is  only about 13.7 billion years old.

We have also a knowledge of large numbers in every day life. Here are some examples:

  • the number of bits in a computer 500-1000GB hard disk is about 10^{13}.
  • the number of cells in a human body is more than 10^{14}
  • the number of neuronal connections in the human brain is approximately 10^{14}.
  • The Avogadro’s constant is 6.022 \times 10^{23} mol-1

The knowledge on large numbers enables us to visualize the universe and answer problems about long time and large quantities. It gives us an understanding of things that are beyond the ordinary.

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