Math Problem Statement
Solution
Let's classify the numbers from the table as either rational or irrational:
-
−18π:
- π (pi) is an irrational number because it cannot be expressed as a fraction of two integers.
- −18π is the product of an irrational number (π) and a rational number (−18), which results in an irrational number.
-
−2√3:
- √3 (square root of 3) is irrational because it is not a perfect square and cannot be expressed as a fraction.
- −2√3 is the product of a rational number (−2) and an irrational number (√3), which results in an irrational number.
-
−92.45:
- This is a terminating decimal, which can be expressed as a fraction (−9245/100), meaning it is a rational number.
-
√49:
- √49 (square root of 49) is a perfect square, equal to 7, which is a rational number.
- So, √49 is a rational number.
-
−70.49:
- This is a terminating decimal, which can be expressed as a fraction (−7049/100), meaning it is a rational number.
Final classification:
- −18π → irrational
- −2√3 → irrational
- −92.45 → rational
- √49 → rational
- −70.49 → rational
Would you like any further details or explanations?
Here are 5 related questions you might want to consider:
- What is the difference between rational and irrational numbers?
- How do you prove that a number like π is irrational?
- Are all square roots irrational?
- How can you express a terminating decimal as a fraction?
- What happens when you multiply a rational number by an irrational number?
Tip: Remember, any terminating or repeating decimal is always rational because it can be expressed as a fraction!
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Math Problem Analysis
Mathematical Concepts
Rational Numbers
Irrational Numbers
Decimals
Square Roots
Formulas
A rational number is any number that can be expressed as a fraction.
An irrational number is a number that cannot be expressed as a fraction.
Theorems
A terminating decimal is a rational number.
The product of a rational and an irrational number is irrational.
Perfect squares have rational square roots.
Suitable Grade Level
Grades 7-9
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