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Rational Numbers Quiz

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Questions and Answers

What is a rational number?

A number that cannot be expressed as a fraction

A number that can only be expressed in decimal form

A number that can be expressed as the quotient of two integers (correct)

A number that has an infinite decimal expansion

What is the set of all rational numbers usually denoted by?

Q (correct)

Which of the following is true about rational numbers?

They cannot be expressed as fractions

Their decimal expansion either terminates or begins to repeat (correct)

They are not real numbers

Their decimal expansion is always infinite

Which of the following numbers is a rational number?

$-3/7$ Signup and view all the answers

What is true about the base in which a rational number's decimal expansion repeats?

It repeats in every integer base Signup and view all the answers

What does the term 'incommensurable' mean in the context of irrational numbers?

There is no common measure for the lengths of two line segments Signup and view all the answers

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

The ratio of a circle's circumference to its diameter Signup and view all the answers

What distinguishes irrational numbers from rational numbers?

Irrational numbers cannot be expressed as the ratio of two integers Signup and view all the answers

Which of the following is true about the square roots of natural numbers?

All square roots of natural numbers, other than of perfect squares, are irrational Signup and view all the answers

How can irrational numbers be expressed?

In positional notation, notably as a decimal number Signup and view all the answers

What does the prefix 'ir-' signify in the term 'irrational numbers'?

Negative or privative Signup and view all the answers

What is the relationship between the ratio of lengths of two line segments and irrational numbers?

The ratio is described as incommensurable if it is an irrational number Signup and view all the answers

Which of the following is NOT an example of an irrational number?

The square root of a perfect square Signup and view all the answers

What does it mean for two line segments to be incommensurable?

There is no length that could be used to express the lengths of both of the two given segments as integer multiples of itself Signup and view all the answers

What is the positional notation of irrational numbers primarily expressed as?

A decimal number Signup and view all the answers

Study Notes

Rational Numbers in Mathematics

A rational number is a number expressed as the quotient or fraction of two integers.
It consists of a numerator and a non-zero denominator.
Examples of rational numbers include -3/7 and 5/1.
The set of all rational numbers is denoted by Q or blackboard bold Q.
Rational numbers are also considered real numbers.
Rational numbers with terminating decimal expansions or repeating sequences of digits are considered rational.
This applies to all integer bases, including binary and hexadecimal.
A real number that is not rational is called an irrational number.
Irrational numbers cannot be expressed as fractions and have non-repeating decimal expansions.
Examples of irrational numbers include √2 and π.
Rational numbers are a subset of real numbers, while irrational numbers are a separate subset.
The distinction between rational and irrational numbers is important in various mathematical calculations and proofs.

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Description

Test your knowledge of rational numbers with this quiz! Learn about the definition, properties, and examples of rational numbers, and see how well you understand this important concept in mathematics.