SECTION 1.1
A set is a collection of objects.
The set of natural numbers is {1,2,3,4,5,….}
The set of whole numbers is {0,1,2,3,4,5,…}
Whole numbers are used for counting objects (such as money, but not cents!) However, they
do not include fractions or decimals.
The digits in a whole number have place value. In the American Number system, digits are
separated into groups of three, starting from just to the right of the ones digit. For more
explanation, see http://www.absoluteastronomy.com/topics/Decimal_separator#encyclopedia
Place
Value
3 4 5
ThreeDigit
Groups
(separated
by commas)
5 7 6
4 0 2
8
9 7
4 1 5
Ones group
Thousands group
Millions group
Billions group
Trillions group
Verbal Form:
30,542 = Thirty thousand, five hundred forty-two.
(Notice we don’t use the word “and”.)
Standard Notation:
Uses only digits (0 through 9) and commas to state the number.
16 million = 16,000,000
Expanded Form:
States the standard form of each place value.
31,567
3 is the place value for ten thousands so this represents 30,000
1 is the place value for thousands, so this represents
1,000
5 is the place value for hundreds, so this represents
500
6 is the place value for tens, so this represents
60
7 is the place value for ones, so this represents 7 ones or
7
31, 567 in Exanded Form is 30,000 + 1,0000 + 500 + 60 + 7
Rounding Whole Numbers:
Step 1: Locate the “rounding digit”, which is the digit at the place value you are rounding to.
Step 2: Look at the digit directly to the right of the rounding digit. This is the test digit. If the test
digit is < 5 (less than 5), keep the rounding digit the same and change all digits to the right of it
to 0.
If the test digit is ≥5 (greater than or equal to 5), then increase the rounding digit by 1 and
change all the digits to the right of it to 0.
On a number line, numbers are written so that ascending numbers are to the right. 10 is to the left
of 20 on the number line, so 20 is greater than 10 (20 > 10). It can also be stated that
descending numbers are to the left, so 10 is less than 20 (10 < 20)
0
10
20
30
40
50
48
Ask "is 48 closer to 40 or 50?" It is closer to 50, it is about 50.
0
10
20
30
40
50
1888
Ask "is 81 is closer to 80 or 90?" It is closer to 80. It is about 80.
Round off the same way for larger numbers.
0
1000
2000
Is 1888 closer to 1000 or 2000? 1888 is closer to 2000.
Is 43,556 closer to 40,000, or 50,000? Compare the first two numbers.
43 is closer to 40 than 50. It is 40,000.
"Tricky" numbers are those with 5 as the number that decides. Is 650 closer to 600 or 700? On a
number line 650 is half way. Math has a rule for this. When the digit is 5 or greater, round up. When the
digit is less than 5, round down.
Example: Round 24 to the nearest ten. Round 36 to the nearest ten
24
35 Rounds up
Rounds down
0
10
20
30
40
50
You may need to estimate to a certain place. Look at the number in the place to the right. Then round.
Round 684 to the tens place.
The number 4 in the ones place to the right of the tens. It rounds down to 680.
Round 6423:
to the nearest ten is 6420.
to the nearest hundred is 6400.
to the nearest thousand, it is 6000.
Round 589,557:
to the nearest ten, it is ________.
to the nearest hundred, it is _______.
to the nearest thousand, it is 590,000
to the nearest ten thousand is 590,000_.
to the nearest hundred thousand is 600,000.
You can round it to the nearest million, it is 1,000,000.
American Numbering System
USA
Power
of 10
ten
hundred
thousand
ten thousand
hundred thousand
million
101
102
103
104
105
billion
10
trillion
quadrillion
quintillion
sextillion
septillion
octillion
nonillion
decillion
undecillion
duodecillion
tredecillion
quattuordecillion
quindecillion
sexdecillion
septendecillion
octodecillion
novemdecillion
vigintillion
unvigintillion
googol
googolplex
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
66
10
10100
10googol
Numbers in Standard Form
10
100
1,000
10,000
100,000
1,000,000
1,000,000,000
1,000,000,000,000
1,000,000,000,000,000
1,000,000,000,000,000,000
1,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000
1 followed by 39 zeroes
1 followed by 42 zeroes
1 followed by 45 zeroes
1 followed by 48 zeroes
1 followed by 51 zeroes
1 followed by 54 zeroes
1 followed by 57 zeroes
1 followed by 60 zeroes
1 followed by 63 zeroes
1 followed by 66 zeroes
1 followed by 100 zeroes
1 followed by googol zeroes
U.S. NATIONAL DEBT CLOCK
The Outstanding Public Debt as of 17 Aug 2009
at 07:03:15 PM GMT is:
The estimated population of the United States is 306,751,966
so each citizen's share of this debt is $38,069.39.
* Taken from http://www.brillig.com/debt_clock/
That is,
Eleven trillion, six hundred seventy-seven billion, eight
hundred fifty-nine million, eight hundred thirty-nine
thousand, seven hundred ninety-one dollars and nineteen
cents.
Note that the word “and” is not used until I got to the cents (that is, a number to
the right of the decimal point).