Key Standards
MCC8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
MCC8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Number system
Real numbers: This group is made up of all the Rational and Irrational Numbers.
Rational numbers: This is any number that can be expressed as a ratio of two integers. As decimals they terminate or repeat.
Irrational numbers: This is any number that can not be expressed as an integer divided by an integer. These numbers have decimals that never terminate and never repeat with a pattern.
Rational Numbers: A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the
denominator (the number on the bottom) are integers.
Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1.
Irrational Numbers: All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not
as a fraction with integers.
Rational vs. Irrational Quiz
Label the following numbers as either rational or irrational.
1.) pi
2.) 3.14
3.) 5 7
4.) 0.1452317...
5.) 8.7532
6.) 1.33333...
7.) √2
8.) √25
