Question 1Given The Numbers: $\pi, \; 7, \; \sqrt{-4}, \; \frac{2}{5}, \; -25$From The List Given Above, Write Down:1.1.1 A Natural Number1.1.2 An Irrational Number1.1.3 A Non-real Number1.1.4 A Rational Number Which Is Not An Integer1.2

Introduction

In mathematics, numbers are classified into various categories based on their properties and characteristics. Understanding these classifications is essential for solving mathematical problems and making informed decisions in various fields. In this article, we will explore the given numbers: $\pi, \; 7, \; \sqrt{-4}, \; \frac{2}{5}, \; -25$ and classify them into different categories.

Classification of Numbers

1.1 A Natural Number

A natural number is a positive integer that is not a fraction or a decimal. In the given list, the number that fits this category is:

• 7: This is a positive integer and is therefore a natural number.

1.1.2 An Irrational Number

An irrational number is a real number that cannot be expressed as a finite decimal or fraction. In the given list, the number that fits this category is:

• $\pi$: This is a well-known irrational number that cannot be expressed as a finite decimal or fraction.

1.1.3 A Non-Real Number

A non-real number is a complex number that has an imaginary part. In the given list, the number that fits this category is:

• $\sqrt{-4}$: This is a complex number that can be expressed as $2i$, where $i$ is the imaginary unit.

1.1.4 A Rational Number Which Is Not an Integer

A rational number is a real number that can be expressed as a finite decimal or fraction. In the given list, the number that fits this category is:

• $\frac{2}{5}$: This is a rational number that can be expressed as a finite decimal or fraction.

1.2 Discussion

In conclusion, the given numbers can be classified into different categories based on their properties and characteristics. Understanding these classifications is essential for solving mathematical problems and making informed decisions in various fields.

Conclusion

In this article, we explored the given numbers: $\pi, \; 7, \; \sqrt{-4}, \; \frac{2}{5}, \; -25$ and classified them into different categories. We identified a natural number, an irrational number, a non-real number, and a rational number that is not an integer. Understanding these classifications is essential for solving mathematical problems and making informed decisions in various fields.

References

• [1] Wikipedia. (2023). Irrational number. Retrieved from https://en.wikipedia.org/wiki/Irrational_number
• [2] Wikipedia. (2023). Rational number. Retrieved from https://en.wikipedia.org/wiki/Rational_number
• [3] Wikipedia. (2023). Complex number. Retrieved from https://en.wikipedia.org/wiki/Complex_number

Q&A: Classifying Numbers

Q1: What is a natural number?

A natural number is a positive integer that is not a fraction or a decimal. In other words, it is a whole number greater than zero.

Q2: What is an example of a natural number from the given list?

The number 7 is an example of a natural number from the given list.

Q3: What is an irrational number?

An irrational number is a real number that cannot be expressed as a finite decimal or fraction. It has an infinite number of digits that never repeat.

Q4: What is an example of an irrational number from the given list?

The number $\pi$ is an example of an irrational number from the given list.

Q5: What is a non-real number?

A non-real number is a complex number that has an imaginary part. It is a number that cannot be expressed on the real number line.

Q6: What is an example of a non-real number from the given list?

The number $\sqrt{-4}$ is an example of a non-real number from the given list.

Q7: What is a rational number?

A rational number is a real number that can be expressed as a finite decimal or fraction.

Q8: What is an example of a rational number that is not an integer from the given list?

The number $\frac{2}{5}$ is an example of a rational number that is not an integer from the given list.

Q9: What is the difference between a rational number and an irrational number?

A rational number can be expressed as a finite decimal or fraction, while an irrational number cannot be expressed as a finite decimal or fraction.

Q10: How do you classify a number that is not a natural number, but is also not an irrational number?

If a number is not a natural number, but is also not an irrational number, it must be a rational number or a non-real number.

Q11: What is the importance of classifying numbers?

Classifying numbers is essential for solving mathematical problems and making informed decisions in various fields. It helps us understand the properties and characteristics of numbers and how they relate to each other.

Q12: Can you provide examples of other numbers that fit into each category?

Yes, here are some examples of other numbers that fit into each category:

• Natural numbers: 1, 2, 3, 4, 5, ...
• Irrational numbers: e, $\sqrt{2}$, $\pi$, ...
• Non-real numbers: $2i$, $3i$, $4i$, ...
• Rational numbers: $\frac{1}{2}$, $\frac{2}{3}$, $\frac{3}{4}$, ...

Conclusion

In this article, we explored the given numbers: $\pi, \; 7, \; \sqrt{-4}, \; \frac{2}{5}, \; -25$ and classified them into different categories. We also answered some frequently asked questions about classifying numbers. Understanding these classifications is essential for solving mathematical problems and making informed decisions in various fields.

References

• [1] Wikipedia. (2023). Irrational number. Retrieved from https://en.wikipedia.org/wiki/Irrational_number
• [2] Wikipedia. (2023). Rational number. Retrieved from https://en.wikipedia.org/wiki/Rational_number
• [3] Wikipedia. (2023). Complex number. Retrieved from https://en.wikipedia.org/wiki/Complex_number

Keywords: natural number, irrational number, non-real number, rational number, classification of numbers, mathematics.