Understanding Rational Numbers

The video explains rational numbers, which are numbers that can be expressed as a fraction 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 irrational numbers, such as the square root of non-perfect squares, which cannot be expressed as a fraction of two integers. The video concludes with a summary of the characteristics of rational numbers.

What is a rational number?

• A number that is always positive.

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

• A number that is always negative.

• A number that cannot be expressed as a fraction.

Which of the following is a rational number?

• 0.333... (repeating)

• The square root of 2

• Pi (π)

• e (Euler's number)

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Why can't zero be in the denominator of a fraction?

• It makes the fraction undefined.

• It makes the fraction positive.

• It makes the fraction equal to zero.

• It makes the fraction negative.

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Which of the following decimals is considered rational?

• 0.333... (repeating)

• 0.123456789...

• 0.5

• 0.101001000...

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How can repeating decimals be expressed?

• As irrational numbers.

• As a fraction of two integers.

• Only as whole numbers.

• Only as decimals.

What is the fractional representation of 0.3 repeating?

• 1/6

• 1/5

• 1/4

• 1/3

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

• The square root of 3

• 1/2

• The square root of 4

• 0.25

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What makes a number irrational?

• It is always a decimal.

• It is always a whole number.

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

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

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Which of the following is true about the square root of a non-perfect square?

• It is always a rational number.

• It is always a negative number.

• It is always an irrational number.

• It is always a whole number.

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What is the key difference between rational and irrational numbers?

• Both can be expressed as fractions.

• Irrational numbers can be expressed as fractions, rational numbers cannot.

• Neither can be expressed as fractions.

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

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