QUESTION 1:Given: $\sqrt{9+25} - 4 ; \sqrt[3]{-27} ; \frac{2}{3} ; \pi - 4 ; \frac{18}{2} ; \sqrt{-27}$.From The List Given Above, Write Down:1.1.1 A Natural Number.1.1.2 A Negative Irrational Number.1.1.3 A Non-real Number.1.1.4 A Rational

by ADMIN 241 views

In mathematics, numbers can be classified into various categories based on their properties. The given list contains several mathematical expressions, and we need to identify the numbers that fall under specific categories. In this article, we will analyze the given list and categorize the numbers accordingly.

1.1 A Natural Number

A natural number is a positive integer that is not a fraction or a decimal. From the given list, we can identify the following natural number:

  • 182=9\frac{18}{2} = 9

This is a natural number because it is a positive integer.

1.1.2 A Negative Irrational Number

An irrational number is a real number that cannot be expressed as a finite decimal or fraction. A negative irrational number is an irrational number that is less than zero. From the given list, we can identify the following negative irrational number:

  • −27\sqrt{-27}

This is a negative irrational number because it is the square root of a negative number, which is an irrational number, and it is less than zero.

1.1.3 A Non-Real Number

A non-real number is a complex number that is not a real number. From the given list, we can identify the following non-real number:

  • −27\sqrt{-27}

This is a non-real number because it is the square root of a negative number, which is a complex number.

1.1.4 A Rational Number

A rational number is a real number that can be expressed as a finite decimal or fraction. From the given list, we can identify the following rational numbers:

  • 23\frac{2}{3}
  • π−4\pi - 4

However, we need to note that π\pi is an irrational number, and when we subtract 4 from it, the result is still an irrational number. Therefore, π−4\pi - 4 is not a rational number.

Conclusion

In conclusion, from the given list, we have identified the following numbers:

  • A natural number: 182=9\frac{18}{2} = 9
  • A negative irrational number: −27\sqrt{-27}
  • A non-real number: −27\sqrt{-27}
  • A rational number: 23\frac{2}{3}

These numbers fall under specific categories based on their properties, and we have analyzed the given list to identify them accordingly.

References

Keywords

  • Natural number
  • Irrational number
  • Non-real number
  • Rational number
  • Mathematics
  • Numbers
  • Properties of numbers
    Frequently Asked Questions (FAQs) about Numbers =====================================================

In the previous article, we identified numbers from a given list and categorized them based on their properties. In this article, we will answer some frequently asked questions (FAQs) about numbers to provide a better understanding of the concepts.

Q: What is the difference between a natural number and a whole number?

A: A natural number is a positive integer that is not a fraction or a decimal. A whole number, on the other hand, includes all natural numbers, as well as zero. In other words, a whole number is a number that is not a fraction or a decimal, and it can be positive, negative, or zero.

Q: What is an irrational number?

A: An irrational number is a real number that cannot be expressed as a finite decimal or fraction. Examples of irrational numbers include the square root of 2, pi, and e.

Q: What is a rational number?

A: A rational number is a real number that can be expressed as a finite decimal or fraction. Examples of rational numbers include 3/4, 2/3, and 1/2.

Q: What is a non-real number?

A: A non-real number is a complex number that is not a real number. Examples of non-real numbers include the square root of -1, i, and any complex number that has an imaginary part.

Q: Can a number be both rational and irrational?

A: No, a number cannot be both rational and irrational. A number is either rational or irrational, but not both.

Q: What is the difference between a real number and a complex number?

A: A real number is a number that can be expressed on the number line, and it includes all rational and irrational numbers. A complex number, on the other hand, is a number that has both a real part and an imaginary part. Examples of complex numbers include 3 + 4i and 2 - 3i.

Q: Can a number be both real and complex?

A: No, a number cannot be both real and complex. A number is either real or complex, but not both.

Q: What is the importance of understanding numbers?

A: Understanding numbers is crucial in mathematics and other fields, as it helps us to solve problems, make calculations, and analyze data. Numbers are the building blocks of mathematics, and they are used to describe the world around us.

Conclusion

In conclusion, numbers are an essential part of mathematics and other fields. Understanding numbers and their properties is crucial for solving problems, making calculations, and analyzing data. We hope that this article has provided a better understanding of numbers and their properties.

References

Keywords

  • Numbers
  • Properties of numbers
  • Natural numbers
  • Whole numbers
  • Irrational numbers
  • Rational numbers
  • Non-real numbers
  • Real numbers
  • Complex numbers
  • Mathematics