Understanding Whole Numbers and Addition

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:

Ones

Tens

Hundreds

Thousands

Ten thousands

Hundred thousands

Millions

Ten Millions

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

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:
Twentythree
thousand one hundred and fortyseven
Example
You have just won the lottery worth seventysix million two hundred forty
thousand one hundred twentyone. Write down this number in standard
notation.
Solution
76,240,121

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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