find the value of x in 11x = Pi

Question

I am confused if my answer is correct or not. I came up to the answer 0.2856 because I substitute Pi as (3.1416).

 

But one of my friend said that I am not correct because we cannot put 3.1416 as the exact value because it is an infinite number. He told me that x = Pi/11 is enough for the answer.

 

Kindly advice me which one is the correct answer. I would really appreciate your vast help.

 

Thanks in advance.

 

 

Answer 1

The teacher/boss/customer/problem may determine whether you use "Pi" or "∏" or "3.14" or "3.1415926" or other.  As Jon P. said, they are all approximations.
 
Just a note about what I call "magic numbers."  Many problems (especially on standardized tests) will use a radius of 7. or 14, or 21.  If you use 3.14 for Pi, you will have some calculating to do.  If you use 3.1415926, you may need a calculator or a computer.  But if you use 22/7 to approximate Pi, you may cancel the 7 and proceed with solving the problem (don't waste time).

Answer 2

It depends on how the question is phrased.  Sometimes you are asked to round the answer to the nearest tenth or hundredth, or to a certain number of decimal places.  If that's the case, then your way of doing it is correct.  But you have to make sure that you use enough decimal places in your approximation of π to satisfy the requirements of the question -- and then round your answer to the number of places you were asked.

 

If you weren't asked to round the answer, and your teacher doesn't have a standard policy that you should round, then you should assume that they want the exact answer.  In that case your friend is right.

 

HOWEVER, it is NOT an infinite number.  An infinite number is one that is greater than any number you can name, which is not the case for π.  It is correct to say that π has an infinitely long decimal representation.  No decimal value that stops after some number of places can be the exact value of π.  So we just use the symbol π to represent the exact value.