# Thread: Approximate Each Number...Part B

1. ## 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) =

2. Originally Posted by magentarita
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!)

3. ## thanks..........

Originally Posted by HallsofIvy
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.