Classify the number below. Select all that apply.*1 pointReal NumberIrrationalRationalIntegerWholeNatural
Question
Classify the number below.
Select all that apply.
1 point
- Real Number
- Irrational
- Rational
- Integer
- Whole
- Natural
Solution
To classify the number, we need to understand the definitions of each category:
- Real Number: Any number that can be found on the number line. This includes both rational and irrational numbers.
- Irrational: A number that cannot be expressed as a fraction of two integers. Its decimal form is non-repeating and non-terminating.
- Rational: A number that can be expressed as a fraction of two integers. Its decimal form either terminates or repeats.
- Integer: A whole number that can be positive, negative, or zero, but not a fraction.
- Whole: A non-negative integer (0, 1, 2, 3, ...).
- Natural: A positive integer (1, 2, 3, ...).
Since the specific number to classify is not provided in the question, let's consider a few examples:
Example 1: The number 5
- Real Number: Yes, 5 is a real number.
- Irrational: No, 5 is not irrational because it can be expressed as 5/1.
- Rational: Yes, 5 is rational because it can be expressed as a fraction (5/1).
- Integer: Yes, 5 is an integer.
- Whole: Yes, 5 is a whole number.
- Natural: Yes, 5 is a natural number.
Example 2: The number -3
- Real Number: Yes, -3 is a real number.
- Irrational: No, -3 is not irrational because it can be expressed as -3/1.
- Rational: Yes, -3 is rational because it can be expressed as a fraction (-3/1).
- Integer: Yes, -3 is an integer.
- Whole: No, -3 is not a whole number because whole numbers are non-negative.
- Natural: No, -3 is not a natural number because natural numbers are positive.
Example 3: The number √2
- Real Number: Yes, √2 is a real number.
- Irrational: Yes, √2 is irrational because it cannot be expressed as a fraction of two integers.
- Rational: No, √2 is not rational.
- Integer: No, √2 is not an integer.
- Whole: No, √2 is not a whole number.
- Natural: No, √2 is not a natural number.
To classify a specific number, you would follow these steps and apply the definitions accordingly.
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