UShort Unsigned 16…bit integer； the smallest value is 0； and the largest value is 65535 Short Signed 16…bit integer； the smallest value is –32768； and the largest value is 32767 UInteger Unsigned 32…bit integer； the smallest value is 0； and the largest value is 4294967295 Integer Signed 32…bit integer； the smallest value is –2147483648； and the largest value is 2147483647 ULong Unsigned 64…bit integer； the smallest value is 0； and the largest value is 18446744073709551615 Long Signed 64…bit integer； the smallest value is –9223372036854775808； and the largest value is 9223372036854775807 Single 32…bit floating…point number； the smallest value is –3。4x1038； and the largest value is 3。4x1038； with a precision of 7 digits Double 64…bit floating…point number； the smallest value is –1。7x10308； and the largest value is 1。7x10308； with 15 to 16 digits of precision Decimal Special 128…bit data type； the smallest value is 1。0x10–28； and the largest value is 1。0x1028； with at least 28 significant digits of precisiona a The Decimal type is often used for financial data because sometimes a calculation will result in one penny less than the correct result （for example； 14。9999； instead of 15。00） due to rounding errors。 …………………………………………………………Page 67…………………………………………………………… 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 45 With so many variations of number types available； you may be wondering which ones to use and when。 The quick answer is that it depends on your needs。 When performing scientific calculations； you probably need to use a Double or Single。 If you are calculating mortgages； you probably need to use a Decimal。 And if you are performing set calculations； you probably should use an Integer or a Long。 It all depends on how accurate you want to be； or how much numeric precision you want。 Numeric precision is an important topic and should never be dealt with lightly。 Consider the following example： every country takes a census of its people； and when the census is piled； we learn some interesting facts。 For example； in Canada； 31％ of people will divorce。 Canada has a population clock that says every minute and 32 seconds； someone is born。 At the time of this writing； the population was 32；789；736。 Thus； at the time of this writing； 10；164；818 people will divorce。 Think a bit about what I just wrote。 I said that there is a direct relationship of people who will divorce to the number of births in Canada （31％； in fact）。 You should be amazed that the births and divorces are timed to the point where 10；164；818—not 10；164；819 nor 10；164；820—people will divorce。 Of course； I’m being cynical and just trying to make the point that numbers are just that： numbers that you round off。 I can’t say 10；164；818 people will divorce； because I can’t be that accurate without performing an actual count。 I could probably say 10；164；818 plus or minus 100；000 will divorce。 Using the plus or minus； the range is 10；064；818 to 10；264；818； or roughly speaking； 10。2 million people。 The number 10。2 million is what a newsperson would report； what literature would say； and what most people would use in conversation。 So； if I add 10。2 million and 1；000； can I say that the total is 10；201；000？ The 10。2 is a roundoff to the nearest tenth of a million； and adding a 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。 …………………………………………………………Page 68…………………………………………………………… 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