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