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.

Play the game.

Which of the following are Rational numbers?

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