How high can you count on your fingers?
How high can you count on your fingers? It seems like a question with an obvious answer. After all, most of us have ten fingers -- or to be more precise, eight fingers and two thumbs. This gives us a total of ten digits on our two hands, which we use to count to ten. But is that really as high as we can go? James Tanton investigates.
Answer the following questions:
If one can readily bend one's fingers into four states - down, slightly down, slightly up, and up - what is the highest number you can represent with ten fingers in a base-4 positional notational system?
Although the placement of symbols now has some significance, this version of the Roman numeral system is still not a system using place-value as we know it today. To illustrate how difficult computation is without the convenience of proper place-value, determine XCVI + IX + CDIX + CCXXIV (using only Roman numerals in your scratch work)
In our place-value system, each of the numbers 10, 100, 1000, 10000, .... uses the same two symbols, yet the sizes of the numbers represented grow ten-fold in value. In 1938, Milton Sirotta, nephew of American mathematician Edward Kasner, coined the term "googol" for the number 1 followed by one hundred zeros, and the term "googolplex" for the number 1 followed by a googol zeros. Is the estimated number of atoms in the observable universe smaller or larger than a googolplex?
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