Rational and Irrational Numbers

The video explains rational numbers, which can be expressed as fractions of two integers. It covers examples of whole numbers, decimals, and zero as rational numbers, and explains that repeating decimals are also rational. The video discusses square roots, highlighting that non-perfect squares are irrational. It concludes with a summary of rational numbers and their characteristics.

What is a rational number?

• A number that is always negative.

• A number that can be written as a fraction of two integers.

• A number that cannot be expressed as a fraction.

• A number that is always positive.

Which of the following is a characteristic of a rational number?

• It must be greater than zero.

• It can only be a whole number.

• Its decimal form either terminates or repeats.

• It cannot be negative.

How can the number 6 be expressed as a rational number?

• 6 over 0

• 6 over 1

• 6 over 6

• 6 over 12

Which of the following decimals is a rational number?

• 0.333... (repeating)

• 0.101001000...

• 0.123456789...

• 0.314159...

Why is zero considered a rational number?

• Because it is a negative number.

• Because it cannot be expressed as a fraction.

• Because it is a positive number.

• Because it can be expressed as 0 over 1.

What is the fractional representation of the repeating decimal 0.3?

• 1/3

• 1/4

• 1/2

• 1/5

Which of the following is a rational number?

• The square root of 5

• The square root of 4

• The square root of 3

• The square root of 2

What makes a number irrational?

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

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

• Its decimal form terminates.

• Its decimal form repeats.

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

• The square root of 16

• The square root of 9

• The square root of 25

• The square root of 2

What is the key difference between rational and irrational numbers?

• Rational numbers are always less than 1, while irrational numbers are greater than 1.

• Rational numbers are always positive, while irrational numbers are negative.

• Rational numbers are always whole numbers, while irrational numbers are decimals.

• Rational numbers can be expressed as fractions, while irrational numbers cannot.