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Math Help - Approximate Each Number...Part B

  1. #1
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    Approximate Each Number...Part B

    The instructions given in the textbook are as follows:

    Approximate each number using a calculator. Express your answer rounded to three decimal places.

    My Question:

    Is there a way to approximate each number below WITHOUT usinga calculator?

    If so, how is this done?

    (1) 5^(1.7) =

    (2) e^(-0.85) =
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  2. #2
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    Quote Originally Posted by magentarita View Post
    The instructions given in the textbook are as follows:

    Approximate each number using a calculator. Express your answer rounded to three decimal places.

    My Question:

    Is there a way to approximate each number below WITHOUT usinga calculator?

    If so, how is this done?

    (1) 5^(1.7) =

    (2) e^(-0.85) =
    Yes, people used to do problems like this in years "BC" (before calculators). However, it involves using tables of logarithms or doing complicated roots.
    For example, 5^(1.7)= 5*5^.7. .7= 7/10 = 700/1000 and 1000 is reasonably close to 2^10= 1024. find the 700 power of 5 and then take the square root 10 times! That gives 15.0239 whereas, by calculator, 5^1.7= 15.4258, approximately.

    (I confess I used a calculator to find the 700 power of 5 and then 10 square roots. YOU can spend hours doing those by hand!)
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  3. #3
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    thanks..........

    Quote Originally Posted by HallsofIvy View Post
    Yes, people used to do problems like this in years "BC" (before calculators). However, it involves using tables of logarithms or doing complicated roots.
    For example, 5^(1.7)= 5*5^.7. .7= 7/10 = 700/1000 and 1000 is reasonably close to 2^10= 1024. find the 700 power of 5 and then take the square root 10 times! That gives 15.0239 whereas, by calculator, 5^1.7= 15.4258, approximately.

    (I confess I used a calculator to find the 700 power of 5 and then 10 square roots. YOU can spend hours doing those by hand!)
    Thanks for the tip and for the math history mini lesson.
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