SOLUTION: Estimate 247^9 without using a calculator. I asked my teacher and she said a hint was 200 < 247 < 300. I'm still really stuck. Please help?
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-> SOLUTION: Estimate 247^9 without using a calculator. I asked my teacher and she said a hint was 200 < 247 < 300. I'm still really stuck. Please help?
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Question 1209409: Estimate 247^9 without using a calculator. I asked my teacher and she said a hint was 200 < 247 < 300. I'm still really stuck. Please help? Answer by math_tutor2020(3817) (Show Source):
Raising each part to the 9th power will not flip the inequality signs.
To estimate 2479, we need to compute 2009 and 3009
Which in turn means we need 29 = 512 and 39 = 19683
Both of which can be computed without a calculator when given enough time.
2009 = (2*102)9
2009 = 29*(102)9
2009 = 512*102*9
2009 = 512*1018
2009 = 5.12*102*1018
2009 = 5.12*102+18
2009 = 5.12*1020
This massive number is 512 followed by 18 zeros.
3009 = (3*102)9
3009 = 39*(102)9
3009 = 19683*1018
3009 = 1.9683*104*1018
3009 = 1.9683*104+18
3009 = 1.9683*1022
This massive number is 19683 followed by 18 zeros.
We go from this
2009 < 2479 < 3009
to this
5.12*1020 < 2479 < 1.9683*1022
Since the numbers involved are so large, I recommend to keep things in scientific notation.
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