Recognizing rational and irrational numbers

Recognizing rational and irrational numbers
Description
Exercise Name:	Recognizing rational and irrational numbers
Math Missions:	8th grade (U.S.) Math Mission, Pre-algebra Math Mission, Mathematics I Math Mission, Algebra I Math Mission, Mathematics II Math Mission
Types of Problems:	1

The Recognizing rational and irrational numbers exercise appears under the 8th grade (U.S.) Math Mission, Pre-algebra Math Mission, Mathematics I Math Mission, Algebra I Math Mission, Mathematics II Math Mission. This exercise allows practice recognizing the difference between rational and irrational numbers.

Types of Problems

There is one type of problem in this exercise:

1. Determine if the number is rational and irrational: This problem provides a number. The user is asked to evaluate if it is rational or irrational.

   

   Determine if the number is rational and irrational

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-square 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 with division, encouraging users to find the repetition spot in numbers such as ${\frac{1}{7}=0.142857}$.
2. Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers!