Math Problem Statement
Solution
Let's classify each number in the table as either rational or irrational:
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: , so . Since is a whole number, it's a rational number.
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: This represents the mixed number , which can be written as . Since it’s a ratio of two integers, it is a rational number.
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: is a non-perfect square and its decimal representation is non-repeating and non-terminating. Therefore, it is an irrational number.
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: This is already in fractional form. Since it is a ratio of two integers, it is a rational number.
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: Since is an irrational number, multiplying it by any non-zero number (like ) still results in an irrational number.
Here’s the completed classification:
Expression | Rational | Irrational |
---|---|---|
✔ | ||
✔ | ||
✔ | ||
✔ | ||
✔ |
Let me know if you need more details or have any questions!
Related Questions:
- How do you determine if a square root is rational or irrational?
- What makes a number rational?
- Can a negative number be irrational?
- How does the multiplication of rational and irrational numbers behave?
- Why is classified as an irrational number?
Tip:
Remember, a rational number can always be written as a fraction of two integers, while an irrational number cannot be expressed this way, and its decimal form is non-repeating and non-terminating.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Rational Numbers
Irrational Numbers
Square Roots
Pi
Formulas
A rational number can be expressed as the ratio of two integers.
An irrational number cannot be written as a simple fraction.
Square roots of non-perfect squares are irrational.
Theorems
A number is rational if it can be written as a fraction of two integers.
Pi (π) is irrational.
Suitable Grade Level
Grades 6-8