Identifying Rational vs. Irrational Numbers

The video tutorial explains the concept of irrational numbers, which cannot be expressed as a ratio of two integers. It provides examples such as the square root of 8 over 2 and pi, highlighting their irrational nature. The tutorial contrasts these with rational numbers like 5.0 and 0.325, which can be expressed as fractions. It also covers repeating decimals, showing they are rational by converting them into fractions. Finally, it demonstrates how mixed numbers like 8 and 1/2 are rational by converting them into improper fractions.

What makes a number irrational?

• It is a whole number.

• It is a repeating decimal.

• It cannot be expressed as a ratio of two integers.

• It can be expressed as a ratio of two integers.

Is the square root of 8 over 2 rational or irrational?

• A whole number

• None of the above

• Rational

• Irrational

Which of the following is an example of an irrational number?

• The square root of 8 over 2

• 5.0

• 0.325

• 7.777777...

Which statement is true about irrational numbers?

• They are always whole numbers.

• They can be expressed as a ratio of two integers.

• They include numbers that repeat indefinitely.

• They cannot be expressed as a ratio of two integers.

Why is pi considered an irrational number?

• It is a perfect square.

• It goes on forever without repeating.

• It can be expressed as a ratio of two integers.

• It is a repeating decimal.

Can 5.0 be considered a rational number?

• No, because it cannot be expressed as a ratio of two integers.

• Yes, because it is a whole number.

• No, because it is a decimal.

• Yes, because it can be expressed as 5/1.

How can 0.325 be classified?

• A repeating decimal

• A perfect square

• Irrational

• Rational, as it can be expressed as 325/1000.

What indicates that a decimal is repeating?

• It ends after a few decimal places.

• It goes on forever without repeating.

• It can be expressed as a ratio of two integers.

• It has a pattern that repeats indefinitely.

Is 7.777777... considered rational or irrational?

• Rational, because it is a repeating decimal.

• Irrational, because it goes on forever.

• Rational, because it is a whole number.

• Irrational, because it cannot be expressed as a ratio of two integers.

How is 8 and 1/2 represented as a rational number?

• As 8.5

• As 17/2

• As an irrational number

• Cannot be represented as a rational number