Name_____________________
Teacher___________________
Period____________________

A rational number is any real number that can be expressed as the ratio of two integers a
, where b is not equal to zero. b
Examples:
A rational number can be expanded so that the decimals either repeat or terminate. In order to convert a fraction to a repeating decimal, use long division and divide the numerator by the denominator.
Class Examples:
1.) Determine if 5
12 is a rational number and convert it to a decimal.
2.) Determine if 3
8 is a rational number and convert it to a decimal.
3.) Determine if 
3
2
5
is a rational number and convert it to a decimal.

Some square roots are also rational. Any number that has a whole-number square root is a perfect square.
Examples:
All rational numbers can be represented on a number line. To plot rational numbers on a number line, first convert them to the same form.
Class Examples:
4.) Plot and label a point for each rational number below on the number line.

2
2
,
1
3
4
, 
0 .
25
,
4
,
1
9
,
72 .
5 %
-1 0 1 2
5.) Plot and label a point for each rational number below on the number line.
4
15
, 6
3
, 
2
1
4
,
9
,
65 %
, 
1 .
75
-3 -2 -1 0 1 2 3

An irrational number is any real number that cannot be expressed as the ratio of two integers a
, where b is not equal to zero. An irrational number can be b expressed as infinite, non-repeating decimal.
Class Examples:
1.) The value of the number pi ( irrational number.
 ) is 3.1459265358… Explain why  is an
The square roots of positive numbers that are not perfect squares are also irrational. You can estimate the value of a square root by deciding which two perfect squares it lies between and then using guess and check to estimate its value more precisely.
2.) Explain why
2 is irrational. Then estimate its value.
3.) Graph the approximate location of
34
on a number line.

4.) Estimate the value of
2 10
5.) Estimate the value of  2 .
.
6.) Estimate the value of
18
.
2
7.) The area of a square is 67 square meters. Find the exact length, in meters, of one side of the square then graph the value on the number line.

Sometimes, you may need to compare or order rational and irrational numbers. The symbols below will help you do this:
> means “is greater than”
< means “is less than”
= means “is equal to”
To compare rational and irrational numbers convert the numbers to decimal form.
Then compare the digits to determine which is greater.
Class Examples:
1.) Which symbol (< , > , =) makes this sentences true?
7.745966…
59
2.) Order the numbers below from least to greatest. Graph on the number line below.
28 %
, 
2
1
2
,
2
7
, 
9
-3 -2 -1 0 1 2 3

3.) Order the following numbers from least to greatest.
 ,
3
1
3
,
14
4.) Order the following numbers from least to greatest.

1
9
,
5
, 
0 .
8
,
3 .
5