TURBO-LESSONS - A Pascal Tutorial        Version 1.01    Page 74


TURBO-LESSON 16:   REAL NUMBERS

OBJECTIVES - In this lesson, you will learn about:

1.  Range of Real Numbers
2.  Input/Output of Real Numbers
3.  Calculations with Real Numbers
4.  Calculations with Integers and Real Numbers


1.  Range of Real Numbers

For business processing (dollar amounts), and scientific 
processing, integers alone are not adequate.  Decimal numbers and 
sometimes numbers in scientific notation are needed.

TURBO provides Real Numbers with 11 significant digits of 
precision in the range:

    1E-38 to 1E+38

(The BCD version of TURBO provides 18 significant digits and a 
range of  1E-63 to 1E+63, but this set of TURBO-LESSONS deals 
with the more limited range above.)

##### DO:

Run PROG16.

Enter 444.333222111 and examine the result presented in 
scientific notation.

How many digits are retained before the E?  (I counted 11, 
including digits on both sides of the decimal point.)

This is the 11 significant digits of precision.  Note that the 
last 1 you entered was dropped.
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2.  Input/Output of Real Numbers.

You will need to know what to expect with various combinations of 
input and output of real numbers.

##### DO:

Run PROG16.  

Enter 444.333222111 and study the various outputs.

When the real number, A, is output without any formatting, 
scientific notation is used:

4.4433322211 are the significant digits.

E+02   means multiply by 10 to the 2nd power to get the number.

If you want the number presented in some other form, you can add 
the :w:d formatting to the name of the variable to print.

:w   Width of the print field
:d   Decimal positions to print

WriteLn(A:10:2);  This statement would print the number, A, in a 
print field 10 characters wide, with 2 decimal positions.

Look at the outputs on the screen again.  The formats used are 
printed at the left.  Square brackets are printed to show the 
width of the field and where the numbere is printed (left or 
right-justified).

:-w   Width of print field, left-justify the number.

Notice the use of the minus sign to force printing of the number 
at the left of the field.

What happens to the print field width when numbers are printed 
left-justified?

##### DO:

Run PROG16 with 3.4567 as input.

What happens when a print format is specified which will not hold 
all of the significant digits?   Is the number rounded?
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3.  Calculations with Real Numbers.

##### DO:

In PROG16 change the ReadLn(A) to ReadLn(B).

Add after ReadLn(B):

A := B + C;

The result printed will be the sum of B, which you enter, and C 
which is a constant, -2.0.

Run the program with 2.34 as input.

Are the results as expected?

In scientific calculations, very large, and very small numbers 
are sometimes needed.  Can you enter these in a convenient form 
without a long string of zeros?

The radius of the earth is 6370000 meters.
This is the same as        6.37 times 100000
Which is the same as       6.37 times 10 to the 6th power
Which may be entered as    6.37E6 or 6.37E06 
                        or 6.37E+6 or 6.37E+06

##### DO:

Run the program with 6.37E6 as input.



Try the other 3 forms listed above.

Are the results the same in all cases?
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##### DO:

Run the program with 6370000 as input.

Does it make any difference whether the number is input in 
scientific notation or in the usual form? 

##### DO:

Run the program with 6.37E7 as input.

What happens when the result is too large for the format?
(Count the character positions used to print A:10:2).

##### DO:

Get a new copy of the original PROG16.

Run the program with 6.37E-6 as input.

Notice the unformatted output is correct, but the formatted 
output shows nothing but zeros.

The result, A, is 0.00000637, with significant digits too far to 
the right to show up in the formatted output.

##### DO:

Change the WriteLn format, A:10:2 to A:10:6.  (Notice there are 
two A:10:2's in the statement).  

Run the program with the following values:

6.37E6,  6.37E-6,  6.37E-4
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4.  Calculations with Integers and Real Numbers.

What happens when you mix Integers and Real numbers in 
calculations?

##### DO:

Get a copy of the original PROG16 and make the following changes:

Change ReadLn(A); to ReadLn(I);

Change the prompt to Write('Enter an Integer: ');

Add after the ReadLn statement:

J := I + C;

Run the program.

What results did you get?

The "Type mismatch" refers to J.  

Since the calculation involves both an integer, I, and a real 
number, C, the result cannot be stored in an integer variable.  
If the result had significant digits after the decimal, they 
would be lost when stored as an integer.  

##### DO:

Change the calculation to:

A := I + C;

Run the program.


NOTE: ON YOUR OWN, YOU MAY WANT TO EXPERIMENT WITH THE WRITELN 
      FORMATS.  CHANGE THE FORMATS TO VARIOUS VALUES AND TRY THEM 
      WITH A VARIETY OF INPUTS.  
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