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thousand means adding a number that is less than the roundoff。 The answer is that I cannot
add 1；000 to 10。2； because the 1；000 is not significant with respect to the number 10。2。 But I
can add 1；000 to 10；164；818； to get 10；165；818； because the most significant value is a single
whole number。
Relating this back to numeric types； it means integer…based numbers have a most signifi
cant single whole number。 Adding 1。5 and 1。2 as whole numbers results in 3； as illustrated in
Figure 2…15。
Let’s extend this concept of significant digits to a floating…point number type； Single； and
consider the example shown in Figure 2…16。 The ｛0｝ construct in the Console。WriteLine（） method
is replaced by the second argument。 If there were a third argument； it would be placed in the
resultant string with ｛1｝； a fourth would be replaced with ｛2｝； and so on。
As shown in Figure 2…16； if you want to keep the precision of adding a small number to a
large number； you will need to switch number types to Double。 But even Double has limits and
can remember only 15 to 16 digits of precision。
If you want even more precision； you could use Decimal； but Decimal is more suitable for
financial calculations。 With financial calculations； you will run into the problem of having very
large numbers added to small numbers。 Imagine being Bill Gates and having a few billion in
your bank account。 When the bank calculates the interest； you will want to know how many
pennies you have accumulated； because pennies； when added over a long period of time； make
a big difference。 In fact； some programmers have “stolen” money from banks by collecting the
fractional pennies and accumulating them。
Now that you’ve seen some of the plexities involved when working with numbers； let’s
finish the calculator。
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46 CH AP T E R 2 ■ L E A R N IN G AB OU T 。 N E T N U M B E R A N D V A L U E T Y P E S
Fractional number one and a half
Public Sub AddFractionalNumbersToWhole（）
Dim total As Integer = CType（1。5； Integer） ＋ _
CType（1。2； Integer）
If （total 2。7） Then
Console。WriteLine（〃Oops； something went wrong〃）
End If
End Sub
Using Ctype（） means to cast a Double
to an Integer。 This results in a
roundoff where 1。2 = 1 and 1。5 = 2。
Had DirectCast（） been used； a
pilation error would result； since
converting a Double to an Integer
requires coercion。
Figure 2…15。 Adding fractions using the Integer data type
Declaring a number with a decimal
A really small number
（。0） automatically creates a floating
point value
Public Sub AddFractionalNumbers（）
Dim value As Single = 10000。0 ＋ 0。000001
Console。WriteLine（〃Value （｛0｝）〃； value）
End Sub
The console displays the number
The variable value is 10；000 because the small number is
the addition of a big insignificant from the perspective of
number to a small Single。 Single can remember only 7
number digits。 10000。000001 is 10 digits of
precision。
Figure 2…16。 Adding fractions using the Single data type
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CH A PT E R 2 ■ L E A R N I N G A B OU T 。 N E T N U M B E R AN D V A L U E T Y P E S 47
Finishing the Calculator
The original declaration of the Add（） method for the calculator worked； but had some serious
limitations on what kinds of numbers could be added。 To finish the calculator； we need to
declare the Add（） method using a different type； and then add the remaining operations。
We could use one of three types to declare the Add（） method：
o Long： Solves the problem of adding two very large numbers like 2 billion； but has the
problem that you cannot add fractional numbers like 1。5 plus 1。5。
o Double： Solves the problem of adding two very large or small numbers； and can be used
to add fractional numbers。 Generally speaking； Double is a good choice； but can suffer
from significance problems if a very large number is manipulated by a very small number。
o Decimal： A generally good approach and suitable for all types of precision； but also the
slowest when adding； subtracting； or performing other mathematical operations。
The simplest all…around numeric data type to use is Double； as it provides good precision
and is relatively fast。 The plete implementation of the calculator is as follows：
Public Class Operations
Public Shared Function Add（ByVal number1 As Double； ByVal number2 As _
Double） As Double
Return number1 ＋ number2
End Function
Public Shared Function Divide（ByVal number1 As Double； ByVal number2 As _
Double） As Double
Return number1 / number2
End Function
Public Shared Function Multiply（ByVal number1 As Double； ByVal number2 As _
Double） As Double
Return number1 * number2
End Function
Public Shared Function Subtract（ByVal number1 As Double； ByVal number2 As _
Double） As Double
Return number1 number2
End Function
End Class
The four operations are methods with different identifiers； but identical method signa
tures； making it easy to remember how to use each method。 Each of the operations would have
an appropriate set of tests verifying the correctness of the implementation。 The tests are not
reproduced here； but they are implemented in the sample source code。 I advise you to take a
quick look at the tests to make sure you understand the individual pieces。
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48 CH AP T E R 2 ■ L E A R N IN G AB OU T 。 N E T N U M B E R A N D V A L U E T Y P E S
The Important Stuff to Remember
In this chapter； you learned about developing a class library that is used to perform some
calculations。 The following are the key points to remember：
o Organization of your thoughts； projects； and features makes all the difference when
writing software。
o When writing software； stay focused。 It is very easy to drift around in software development；
because software lets you stray easily。 A successful developer will always be organized
and focused。
o Software is designed using an architecture that could be implemented top…down or
bottom…up。
o Within an architecture； individual pieces are called ponents； and they