Math Problem Statement
Classify the given numbers as either rational or irrational.
Solution
The image shows a table where you need to classify numbers as either rational or irrational. Let's analyze each number:
-
:
- , which is an integer. Integers are rational numbers.
- Classification: Rational
-
:
- is a terminating decimal, which can be expressed as a fraction. Therefore, it is a rational number.
- Classification: Rational
-
:
- is not a perfect square, so it is an irrational number. The negative sign does not affect the irrationality.
- Classification: Irrational
-
:
- represents a repeating decimal (54.1111...), which can be expressed as a fraction. Repeating decimals are rational numbers.
- Classification: Rational
-
:
- is an irrational number, and multiplying it by any non-zero rational number (such as 14) still results in an irrational number.
- Classification: Irrational
Final Table:
Number | Rational | Irrational |
---|---|---|
☑ | ||
☑ | ||
☑ | ||
☑ | ||
☑ |
Would you like further details on any of these concepts?
Here are some related questions you might be interested in:
- What makes a number rational or irrational?
- How do you convert a repeating decimal into a fraction?
- Can irrational numbers ever be written as fractions?
- What are some other examples of irrational numbers?
- How does the square root of a non-perfect square differ from that of a perfect square?
Tip: Remember, a terminating or repeating decimal is always rational!
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Math Problem Analysis
Mathematical Concepts
Number Classification
Rational Numbers
Irrational Numbers
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8
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