In mathematics, what does it mean when a question asks you to 'evaluate'?

Question

Here is the question:
Evaluate:
3^-2

Does that mean i just have to convert it into normal numbers (e.g 0.03)?
--------------------
Also,
a question says
Estimate:
(4.1 x 10^5) x (7.9 x 10^8)
------------ divided by ---------
(3.8 x 10^8)

So for the estimation, do i change the (4.1 x 10^5) to (4.0 x 10^5), the (7.9 x 10^8) to (8.0 x 10^8) and the (3.8 x 10^8) to (4.0 x 10^8)?

Thanks

Answer 1

I understand "evaluate" as "calculate the value of."



3^(-2) = 1 / 3² = 1 / 9



Estimate means have a good guess !



4 x 8 x 10^13

-----------------

4 x 10^8



8 x 10^5



800,000

Answer 2

For the first part, you're right. In mathematics 'evaluate' means to express numerically.



For the second part, I would do 4 times 8 = 32

10^5 times 10^8 = 10^13

Combining, we have: 32 x 10^13 ==> 3.2 x 10^14



Then - for the denominator -: 4 x 10^8

3/4 = 0.75

8 x 10^5

Answer 3

I agree with all the above mathematicians. Happy New Year !

Answer 4

First part : Yes - you are correct



Second part : Apply some judicious rounding



(4 * 10^5) * (8 * 10^8)

-------------------------------

(4 * 10^8)



The 4 cancels out as does the 10^8 leaving



(1 * 10^5) * (8 * 1)

-------------------------- = 8 * 10^5

1

Answer 5

I agree with the consensus.



Evaluate mean to carry out the operation to its fullest extent.



e.g. evaluate 3^(-2) means to carry out the arithmetic/algebra.



==> 3^(-2) = 1/3^2 = 1/(3*3) = 1/9 (done)



Make sense?



:)

Answer 6

Evaluate just means you only have numbers to work with, so just do the arithmetic. So 3^-2 means first make the exponent positive.....so now you have 1/3^2, and evaluate 3^2 to be 9, so your answer will be:



1/9



You can't evaluate something like 3x + 4x, but you can simplify it to be 7x. Since you don't know what x is, you can't evaluate it! Make sense? =)

Answer 7

You have answered your own questions correctly.



Evaluate simply means "find the numerical value of."



the estimation process you explained is very useful as well. It will make the process of dividing and multiplying these numbers much simplier.

Answer 8

for both the questions you have to solve and find the answer

Answer 9

It just means do it.

Answer 10

LOOK IT UP IN THE DICTIONARY.