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Can you explain the answer of this question below:
Which of the following statement is true?
- A:Every real number is a rational number.
- B:Every real number is irrational.
- C:The real number line contains both rational as well as irrational numbers.
- D:Half the numbers on the number line are rational and the remaining half irrational
The answer is c.
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Can you explain the answer of this question below:Which of the followi...
The real numbers consist of both rational
and irrational numbers. so the other three options are not true as the first one is not true because not only every real number is a rational number but real number is a rational and irrational both. same goes for the second one and the last one option is not true because one half and the other half can be irrational or rational both.
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Can you explain the answer of this question below:Which of the followi...
**Explanation:**
The correct statement among the options is C: The real number line contains both rational as well as irrational numbers.
**Rational Numbers:**
Rational numbers are numbers that can be expressed as a fraction of two integers. In other words, they can be written in the form p/q, where p and q are integers and q is not equal to zero. Rational numbers include integers, fractions, and terminating or repeating decimals.
**Irrational Numbers:**
Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They cannot be written in the form p/q, where p and q are integers and q is not equal to zero. Irrational numbers include non-repeating and non-terminating decimals, such as √2, π, and e.
Now, let's break down the explanation into headings and bullet points:
**Real Number Line:**
- The real number line is a line that represents all the real numbers. It extends infinitely in both the positive and negative directions.
- The real number line includes all rational and irrational numbers.
**Rational Numbers on the Number Line:**
- Rational numbers can be represented on the number line.
- Examples of rational numbers on the number line include integers (such as -3, -2, -1, 0, 1, 2, 3) and fractions (such as 1/2, 3/4, 5/3).
- Rational numbers appear as points that are evenly spaced on the number line.
**Irrational Numbers on the Number Line:**
- Irrational numbers can also be represented on the number line.
- Examples of irrational numbers on the number line include the square root of 2 (√2), pi (π), and Euler's number (e).
- Irrational numbers appear as points that are not evenly spaced on the number line.
- They are located between the rational numbers and do not have a repeating or terminating pattern.
**Conclusion:**
The real number line contains both rational and irrational numbers. Hence, option C is the correct statement.
The correct statement among the options is C: The real number line contains both rational as well as irrational numbers.
**Rational Numbers:**
Rational numbers are numbers that can be expressed as a fraction of two integers. In other words, they can be written in the form p/q, where p and q are integers and q is not equal to zero. Rational numbers include integers, fractions, and terminating or repeating decimals.
**Irrational Numbers:**
Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They cannot be written in the form p/q, where p and q are integers and q is not equal to zero. Irrational numbers include non-repeating and non-terminating decimals, such as √2, π, and e.
Now, let's break down the explanation into headings and bullet points:
**Real Number Line:**
- The real number line is a line that represents all the real numbers. It extends infinitely in both the positive and negative directions.
- The real number line includes all rational and irrational numbers.
**Rational Numbers on the Number Line:**
- Rational numbers can be represented on the number line.
- Examples of rational numbers on the number line include integers (such as -3, -2, -1, 0, 1, 2, 3) and fractions (such as 1/2, 3/4, 5/3).
- Rational numbers appear as points that are evenly spaced on the number line.
**Irrational Numbers on the Number Line:**
- Irrational numbers can also be represented on the number line.
- Examples of irrational numbers on the number line include the square root of 2 (√2), pi (π), and Euler's number (e).
- Irrational numbers appear as points that are not evenly spaced on the number line.
- They are located between the rational numbers and do not have a repeating or terminating pattern.
**Conclusion:**
The real number line contains both rational and irrational numbers. Hence, option C is the correct statement.
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