Rational vs. Irrational Numbers
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Questions and Answers

Which of the following numbers are rational? (Select all that apply)

  • -5/1 (correct)
  • √64 (correct)
  • 9.68 (correct)
  • √6
  • 2.010010001

Which is irrational?

  • 0.333
  • 5.1
  • √8 = 2.8284 (correct)
  • √14 = 7
  • √2 = 4.4

If a square has an area of ______ cm², then one side is 10 cm

100

Flashcards

Rational Number

A number that can be expressed as a fraction, where both the numerator and denominator are integers.

Irrational Number

A number that cannot be expressed as a fraction of two integers. It has an infinite, non-repeating decimal representation.

Repeating Decimal

A decimal that repeats a pattern of digits infinitely.

Non-Terminating Decimal

A decimal that does not terminate or repeat. It continues infinitely without any repeating pattern.

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Square Root

The square root of a number is the value that, when multiplied by itself, equals the original number.

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Algebraic Expression

A mathematical expression that combines numbers, variables, and operations.

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Equation

A statement that shows the equality of two mathematical expressions.

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Scientific Notation

A mathematical representation of a very large or very small number using a base (usually 10) and an exponent.

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Solution Set

The set of all possible values that satisfy an equation or inequality.

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Exponent

A mathematical operation that involves multiplying a number by itself a specified number of times.

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Base

The number that is multiplied by itself in an exponent.

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Pi (Ï€)

The symbol 'Ï€' (pi) represents the ratio of a circle's circumference to its diameter. It is an irrational number approximately equal to 3.14159.

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Calculation

The process of finding the value of an expression or equation.

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Comparing Values

The process of comparing two or more values to determine their relative size.

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Example

A specific example used to demonstrate or illustrate a concept or principle.

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Problem

A problem posed to test understanding or to be solved.

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Explanation

A statement that describes or explains a fact or rule.

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Organization

The systematic arrangement of ideas or information according to a specific plan.

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Section

A section or part of a larger piece of writing.

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Study Notes

Rational vs. Irrational Numbers

  • Rational numbers can be expressed as a fraction (a/b) where a and b are integers and b≠0.
  • Examples include 1.68, -5/4.
  • Irrational numbers cannot be expressed as a fraction. Their decimal representation neither terminates nor repeats.
  • Examples include √6, 2.010010001.

Comparing Values

  • To find the largest value among Ï€, √24, and 4.2, calculate the decimal approximations.

  • Ï€ ≈ 3.14159

  • √24 ≈ 4.89898

  • 4.2

  • √24 has the largest value.

Identifying Rational and Irrational Numbers

  • 0.333... is rational because it's a repeating decimal
  • √8 is irrational because it has a non-repeating, non-terminating decimal expansion.
  • √14 is irrational.

Determining the Area's Side Length

  • If an area is 200 cm², the side length cannot be determined without more information since area is not directly related to side length.

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Description

Test your understanding of rational and irrational numbers with this quiz. Explore concepts such as fractional representations, comparing values, and identifying various number types. Put your mathematical reasoning to the test!

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