1. 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) =

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) pi^(e) =

(2) e^(pi) =
$\pi$ 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 $1024= 2^10$. $\pi^e$ 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
$\pi$ 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 $1024= 2^10$. $\pi^e$ 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?

4. 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 $\pi^e= \pi^2 \pi^{.718}$

--Chris

5. ok....

Originally Posted by Chris L T521
He/she happened to forget a forward slash in the last bracket. It would have generated the image $\pi^e= \pi^2 \pi^{.718}$

--Chris
Thanks for clearing that up for me.