% Problem 1

clear
close all

% a)

3+9

ans =

    12


% b)

2^123

ans =

  1.0634e+037


% This is a floating point approximation to 2^123.  We can force all
% of the digits of this integer to be displayed by converting one of
% the numbers to a symbolic expression.

sym('2')^123
 
ans =
 
10633823966279326983230456482242756608
 

% c)

% We use vpa to display 35 digits of pi^2.

vpa('pi^2', 35)
 
ans =
 
9.8696044010893586188344909998761512
 

% Unlike pi, e is not predefined in MATLAB, but we can generate it by
% taking the exponential of 1.

vpa('exp(1)', 35)
 
ans =
 
2.7182818284590452353602874713526625
 

% d)

a = 22/7

a =

    3.1429

b = 311/99

b =

    3.1414

c = 355/113

c =

    3.1416


a - pi

ans =

    0.0013

b - pi

ans =

 -1.7851e-004

c - pi

ans =

  2.6676e-007


% We see that 355/113 is the best approxinmation to pi.

echo off
diary off