Understanding Irrational Numbers

What is an irrational number?

• An irrational number is a complex number.

• An irrational number is a number that can be expressed as a simple fraction.

• An irrational number is a whole number.

• An irrational number is a real number that cannot be expressed as a simple fraction.

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CCSS.HSN.RN.B.3

Give an example of an irrational number.

• 1.3452

• 1/32

• Square root of 2

• Square root of 36

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CCSS.HSN.RN.B.3

Explain why the square root of 2 is an irrational number.

• The square root of 2 is a prime number.

• The square root of 2 is rational because it can be expressed as a fraction.

• The square root of 2 is an integer number.

• The square root of 2 is an irrational number because it cannot be expressed as a fraction of two integers where the denominator is not zero.

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CCSS.HSN.RN.B.3

Are all square roots irrational? Why or why not?

• Yes

• Only for prime numbers

• Sometimes

• No

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CCSS.HSN.RN.A.1

CCSS.HSN.RN.B.3

How are irrational numbers represented on a number line?

• By plotting them as whole numbers on the number line

• By skipping them altogether on the number line

• By representing them as fractions on the number line

• By approximating their values on the number line.

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Can you convert an irrational number into a fraction? Why or why not?

• No

• Yes, because fractions are a more accurate representation of numbers

• Yes, because all numbers can be converted into fractions

• Yes, because irrational numbers have a finite number of decimal places

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CCSS.HSN.RN.B.3

What is the decimal representation of an irrational number?

• The decimal representation of an irrational number is always a whole number.

• The decimal representation of an irrational number is non-terminating and non-repeating.

• The decimal representation of an irrational number is always a terminating decimal.

• The decimal representation of an irrational number is always a repeating decimal.

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CCSS.HSN.RN.B.3

What is the difference between rational and irrational numbers?

• Rational numbers can be expressed as a ratio of two integers, while irrational numbers cannot be expressed as a simple fraction.

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

• Rational numbers are always integers, while irrational numbers are always fractions.

• Rational numbers have repeating decimal representations, while irrational numbers have non-repeating decimals.

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CCSS.HSN.RN.B.3

How do you determine if a number is irrational?

• See if the number is a prime number

• Check if the number cannot be expressed as a fraction of two integers or if its decimal representation is non-repeating and non-terminating.

• Verify if the number is divisible by 2

• Check if the number is a perfect square

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CCSS.HSN.RN.B.3

Why are irrational numbers important in mathematics?

• Irrational numbers are not important in mathematics

• Irrational numbers are just a theoretical concept with no practical applications

• Irrational numbers fill in the gaps left by rational numbers, providing a more complete number system.

• Irrational numbers are only used in advanced math courses

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