Pre Algebra Place Value
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A Nice Place
Place Value

 Once upon a time there were no numbers. 
 There was the IDEA of numbers, but nobody had a way of writing things down.
 Then people started coming up with symbols to stand for numbers.
 One old-time way maybe you've seen was the Roman system. 
 The Romans said "Hey, we don't need to invent new squiggles. 
 We can just use the ones we already have!" And that's what they did. 
 They said "Let's make the letter I mean one. 
 V can mean five. X can mean ten. L can mean fifty. And so it went. 
 They had a new code. A number code.
 For example:

 VII means seven


 LXXVI means seventy six

 That worked OK until people started doing seroius math.

 MCXVII times LXVI just doesn't cut it!

 So now we use a different system. 
 It was invented in the Middle East. 
 The biggest deal about this system is not the squiggles it uses. 
 The big deal is something called PLACE VALUE.
 Here's how it works. 
 The system uses the numbers we all know. 
 They are called the digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

 The biggest one of these is 9. 
 Without place value, if we needed to write down more than 9 of something,
 we'd be out of luck.
 With place value, when we get to one more than 9 is use the 1 again.
 The big deal is, we put it in a special place so it means ten.
 That special place is called:



 The numbers that are smaller than ten go in a place called:


 If we have a number in the tens column, but no number in the ones column:


 We put a zero in the ones column so everybody knows who is who:

 The zero makes sure that everybody knows 
 that the one is in the TENS COLUMN.
 The zero keeps the one in its place. 
 We sometimes call zeros PLACE KEEPERS.
 We can add columns to the left of the ones we already have. 
 We can do that forever to get bigger and bigger numbers. 
 There is no limit to how big a number we can make. 
 Each 1 in a column is worth as much as ten 1s in the column to its right. 
 The next column to the left is called the HUNDREDS COLUMN
 It is the last single column that has its own special name:

 Why did they make each one in a column worth as much as ten 
 in the column to the right?
 Why not 8 times as much? Why not 62 times as much?
 No special reason. They could have done it that way. 
 If we had 8 or 62 fingers instead of 10, they might have done it that way ...
 The column a number is in also tells you how to say the number.
 If the first number is in the hundreds column, 
 say the number and then the word Hundred. 
 Then go on.
 Next comes the tens column. 
 The tens column is really weird. 
 You should be able to say the number and then some word like ten and go on. 
 No chance. We need more pain. 
 Math types invented a bunch of words for the numbers in the tens column. 
 One word for each number, except for 1 and 0. They are:
2 Twenty
3 Thirty
4 Forty
5 Fifty
6 Sixty
7 Seventy
8 Eighty
9 Ninety
 Now for the number one. 
 A one in the tens column can have a bunch of different names. 
 It depends on what number is in the ones column next to it. 
 The good news is that the name counts for both the one in the tens column
 AND the number in the ones column.  
 The names are:
10 Ten
11 Eleven
12 Twelve
13 Thirteen
14 Fourteen
15 Fifteen
16 Sixteen
17 Seventeen
18 Eighteen
19 Nineteen
 So if the number in the tens column is a 2, 3, 4, 5, 6, 7, 8, or 9
 we use one of those names that ends in "ty".
 Then we deal with the number in the ones column. 
 This one is easy. Just say or write the number.
 If the number in the tens column is a one, 
 we use one of the names above that mostly end in "teen". 
 Hmmm, teen is kind of like saying ten in some other language eh?
 So what about our old pal the zero? 
 Here we get some good news.
 When you get to a zero, just skip it!
 Now with these names we can write the name of the number we had a bit ago.
 It was 328. 
 The way we write it is:
The first number is in the hundreds column, so write the number ... And add the word hundred The number in the tens column is between 2 and 9 so we use a word that ends in TY, In this case the word Twenty. Now just use the regular name for the number in the ones column.
 So swell. Now we can deal with numbers up through the hundreds. 
 What about all of the bigger numbers? 
 What do we do with them?
 I'm glad you asked.
 For numbers bigger than hundreds, 
 we use the hundreds, tens and ones columns again. 
 But this time, we add another word.  
 We are going to use our three columns again and again. 
 Each time we use them, we add a different word. 
 It's kind of important that you learn the first few of these. 
 Here are the first two:

 We make little groups of every three columns.
 The three columns on the right don't have any special name
 you need to remember, but the other groups do. 
 Starting from the right, the second group is called the thousands. 
 The third group is called the millions.
 After that you get to billions and trillions
 and lots of other names that end in "illions". 
 To say these big numbers, 
 just say the name of the three column number from the group
 and add the group name.
 Another little trick we use when we write a great big number as digits
 is to put a comma between each 3 number group.
 Say, here comes a big number now:


 If we put that big number into the grid, we get:

 To say or write the number:
 Start at the left and say the 3 column group number. 
 Then say the group name and move on. 
 So for this puppy we have:


 Did you notice how we just skipped right over the zero in the last group? 
 Tricky eh? We also added commas after the group names. 
 You should do that to be really correct.

   copyright 2005 Bruce Kirkpatrick

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