Flash Cards - Real Numbers

Flash Cards: Real Numbers

This chapter explores real numbers, focusing on key properties such as the Fundamental Theorem of Arithmetic and the concept of irrational numbers, which are crucial for understanding the number system.

Flash Cards - Real Numbers

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What is the Fundamental Theorem of Arithmetic?

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The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be uniquely factored into a product of prime numbers.

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2/10

Give an example of an irrational number.

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√2 is an example of an irrational number as it cannot be expressed as a simple fraction and its decimal representation is non-repeating and non-terminating.

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5/10

Define irrational numbers.

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5/10

Irrational numbers are real numbers that cannot be expressed as a ratio of two integers and have non-repeating, non-terminating decimal expansions.

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6/10

What is the difference between rational and irrational numbers?

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Rational numbers can be expressed as a ratio of two integers and have either terminating or repeating decimal expansions, while irrational numbers cannot be expressed as a ratio of two integers and have non-repeating, non-terminating decimal expansions.

7/10

Can you give an example of an irrational number?

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One example of an irrational number is the square root of 2 (√2).

8/10

What is the Fundamental Theorem of Arithmetic?

8/10

The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be uniquely factored into a product of prime numbers.

9/10

Define irrational numbers.

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Irrational numbers are real numbers that cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions.

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What is the difference between rational and irrational numbers?

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Rational numbers can be expressed as a fraction of two integers and have either terminating or repeating decimal expansions, while irrational numbers cannot be expressed in that form.

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Can you give an example of an irrational number?

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One example of an irrational number is the square root of 2 (√2).

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Explain the concept of prime numbers.

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Prime numbers are natural numbers greater than 1 that are only divisible by 1 and themselves.

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