Thread: Approximate Each Number...Part A

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) pi^(e) =

(2) e^(pi) =

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) pi^(e) =

(2) e^(pi) =

$\displaystyle \pi$ is approximately 3.141592 and e is approximately 2.71828 so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately. .718= 718/1000 and 1000 is close to $\displaystyle 1024= 2^10$. $\displaystyle \pi^e$ will be approximately 3.14 to the 718 power, then square root 10 times. That won't be very good approximation. You might see if you can find a higher power of 10 that is closer to a power of 2. Of course, that's going to be an awful lot of work!

Originally Posted by HallsofIvy

$\displaystyle \pi$ is approximately 3.141592 and e is approximately 2.71828 so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately. .718= 718/1000 and 1000 is close to $\displaystyle 1024= 2^10$. $\displaystyle \pi^e$ will be approximately 3.14 to the 718 power, then square root 10 times. That won't be very good approximation. You might see if you can find a higher power of 10 that is closer to a power of 2. Of course, that's going to be an awful lot of work!

Something is wrong with your math reply when saying "so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately"

Why is the word math in brackets?

Originally Posted by magentarita

Something is wrong with your math reply when saying "so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately"

Why is the word math in brackets?

He/she happened to forget a forward slash in the last bracket. It would have generated the image $\displaystyle \pi^e= \pi^2 \pi^{.718}$

--Chris

Originally Posted by Chris L T521

He/she happened to forget a forward slash in the last bracket. It would have generated the image $\displaystyle \pi^e= \pi^2 \pi^{.718}$

--Chris

Thanks for clearing that up for me.