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Recognizing rational and irrational numbers
Description
Exercise Name: Recognizing rational and irrational numbers
Math Missions: 8th grade (U.S.) Math MissionPre-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 MissionPre-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.

## 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!