Exploring Rational and Irrational Numbers

The video tutorial explains the difference between rational and irrational numbers. It defines rational numbers as those that can be expressed as a ratio of two integers, including fractions, integers, and finite or repeating decimals. Examples are provided to illustrate these concepts. The video also covers irrational numbers, which cannot be expressed as a ratio of two integers, such as non-repeating decimals, square roots that cannot be simplified, and constants like pi and e. The tutorial concludes by summarizing how to identify rational and irrational numbers.

Which of the following is an example of a rational number?

• Pi (π)

• 3/4

• Square root of 2

• e (Euler's Number)

Can every integer be considered a rational number?

• Yes, because they can be expressed as a ratio of integers

• No, integers are not rational

• Only positive integers are rational

• Only negative integers are rational

Which of the following statements is true about rational numbers?

• They can only be positive

• They include the square roots of prime numbers

• They can be expressed as the ratio of two integers

• They have an infinite number of non-repeating decimal places

Is 0.25 considered a rational number?

• No, because it is a decimal

• Yes, but only in certain contexts

• No, because it is not an integer

• Yes, because it can be expressed as a fraction

Which of the following decimals is a rational number?

• 0.333... (repeating)

• Square root of 3

• Pi (π)

• e (Euler's Number)

Is the square root of 9 rational or irrational?

• Irrational, because it cannot be expressed as a fraction

• Irrational, because it involves a square root

• Rational, because it simplifies to an integer

• Rational, because it is a decimal

Why is the square root of 7 considered irrational?

• Because it is a natural number

• Because it cannot be expressed as a fraction of two integers

• Because it is a repeating decimal

• Because it simplifies to an integer

Which of the following is an irrational number?

• 2/3

• 0.75

• Pi (π)

• 1/2

What makes a number irrational?

• Being a whole number

• Having an infinite number of decimal places without repeating

• Being a natural number

• Being a repeating decimal

Can the number e be written as a ratio of two integers?

• No, because it is a natural logarithm base

• Yes, but only in specific mathematical contexts

• No, because it has an infinite number of decimal places

• Yes, because it is a constant