Understanding Whole Numbers and Addition

1. The Number System and Base 10
   
   The number system is constructed based on the principal that we have ten fingers. When we count after 9 we arrive at the two digit number 10.  Similarly after 99 we arrive at a three digit number.  We call the rightmost digit the ones digit, the next one the tens digit, the next one the hundreds digit, etc.  Below is a list of the names of the number places in order from right to left:

    

   1. Ones

   2. Tens

   3. Hundreds
      

   4. Thousands

   5. Ten thousands

   6. Hundred thousands
      

   7. Millions

   8. Ten Millions

   9. Hundred Millions

   Notice that the names are grouped in threes.  This is how we group numbers, using a "," to separate each group of three.   Each group is called a period.

   Example:

           230,508,921

   We can write this number in expanded notation by breaking apart each digit and adding zeros as follows:

           200,000,000 + 30,000,000 + 500,000 + 8,000 + 900 + 20 + 1

   Example:

   Write the number

           400,000,000 + 20,000,000 + 1,000,000 + 70,000 + 6,000 + 500 + 40

   in standard notation.

   Solution:

   We are careful here to include a zero when that digit is skipped.  Notice that the hundred thousands digit and the ones digit are skipped, hence they are zero:

           421,076,540

    

    

2. Reading and Writing Numbers
   
   Writing numbers is especially important for writing checks.  Suppose that you want to buy a car for $23,147.  What should you write on your check?
   
   First remember never to use the word and for whole numbers.  We write the number from each period:
   
           Twenty-three thousand one hundred and forty-seven
   
   Example
   
   You have just won the lottery worth seventy-six million two hundred forty thousand one hundred twenty-one.  Write down this number in standard notation.
   
   Solution
   
           76,240,121
   

3. Addition
   
   Recall that to add whole numbers, we use the method of carrying:
   
   Example
   
           11
           923
       +  478
         1401
   
   Example
   
   You just purchased a snow board for $349, boots for $238 and a Helmet for $89.  What is your total bill?
   
   Solution
   
           12
           349
           238
        +   89
           676
   
   The total bill is $676.
   
   Example
   
   You want to put siding on a new rectangular addition in you home.  If the addition is 15 feet by 18 feet, how much siding must you buy?
   
   Solution
   
   We draw the rectangle and notice that the sides are 15, 15, 18, and 18 feet.  We add these four sides:
   
           2
           15
           15
           18
        + 18
           66
   
   We need to buy 66 feet of siding.
   

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