Question 992047: Which pair of numbers is closer together? 10^10 and 10^50 , or the pair 10^100 and 10^101?
I know 10^100 and 10^101 are much much further apart due to the exponent operating on a much larger scale, but I don't know how to prove this is mathematical notation. My calculator gives maths error for 10^101-10^100, so ideally I would like some algebraic way of proving the solution that doesn't simply rely on typing the numbers in.
Thanks.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Which pair of numbers is closer together? 10^10 and 10^50 , or the pair 10^100 and 10^101?
I know 10^100 and 10^101 are much much further apart due to the exponent operating on a much larger scale, but I don't know how to prove this is mathematical notation. My calculator gives maths error for 10^101-10^100, so ideally I would like some algebraic way of proving the solution that doesn't simply rely on typing the numbers in.
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10^50-10^10 = 10^10[10^40-1]
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10^101-10^100 = 10^100[10-1] = 10^10[10^90]*9
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Since 10^90*9 > 10^40-1, 10^101-10^100 is a greater difference.
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Cheers,
Stan H.
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