Recognizing rational and irrational numbers

The  exercise appears under the 8th Grade Math Mission. This exercises practices recognition of the difference between rational and irrational numbers.

Types of Problems
There is one type of problem in this exercise:


 * 1) Determine which numbers are rational and irrational: This problem provides a list of various types of numbers. The student is asked to classify each as rational or irrational.Rrain1.png

Strategies
The definitions are important, as are an ability to recognize the types of numbers that are consistently rational or irrational.
 * 1) A rational number can be written as a ratio of integers, an irrational number cannot.
 * 2) A rational number has a terminating (or repeating) decimal form, an irrational number does not.
 * 3) Radicals of non-perfect numbers are irrational.
 * 4) Be aware that square roots of perfect squares are integers, and thus rational.
 * 5) Transcendental numbers (like pi and e) are always irrational.

Real-life applications

 * 1) An ability to know which numbers are rational or irrational can help to determine with division, encouraging to students to find the repetition spot in numbers such as 1/7=0.142857.