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parallaxicality
2015-Dec-30, 05:14 PM
For a Wikipedia article. I'm struggling with the math of 10^10^115 times 10^10^10^56. Would multiplying them together make any difference to the larger number at all?

antoniseb
2015-Dec-30, 05:27 PM
For a Wikipedia article. I'm struggling with the math of 10^10^115 times 10^10^10^56. Would multiplying them together make any difference to the larger number at all?
Sure it would... 10^10^115 is about 10^10^10^2.1 so the result would be about 10^10^10^58.1

grapes
2015-Dec-30, 05:48 PM
For a Wikipedia article. I'm struggling with the math of 10^10^115 times 10^10^10^56. Would multiplying them together make any difference to the larger number at all?
Sure it would... 10^10^115 is about 10^10^10^2.1 so the result would be about 10^10^10^58.1
No. The exponent 2.1 only applies to the last ten, not all three (there are different ways to interpret this, but that seems consistent with your numbers). So, 10^10^10^2.1 times 10^10^10^56 would be 10^(10^10^2.1+10^10^56), which is 10^(10^115 + 10^10000000000000000000000000000000000000000000000 0000000000). The first number in that sum has 115 zeroes, the second number has a hundred billion billion billion billion billion billion zeroes. :)

On the other hand, does multiplying a billion by ten make a difference? The exponent "only" changes from nine to ten, but it's still ten times larger than before!