Algebra II Assignment 2: Real Numbers

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Questions and Answers

What is a rational number?

  • A nonterminating, nonrepeating decimal
  • A terminating or repeating decimal (correct)
  • A number that can be expressed as a quotient of two integers (correct)
  • A number that cannot be expressed as a quotient of two integers

What is an irrational number?

  • A repeating decimal
  • A number that cannot be expressed as a quotient of two integers (correct)
  • A terminating decimal
  • A number that can be expressed as a quotient of two integers

Is 1384 a rational number?

Yes

Is π a rational number?

<p>No</p> Signup and view all the answers

-0.28764... is what type of number?

<p>Irrational</p> Signup and view all the answers

Is 0 a rational number?

<p>Yes</p> Signup and view all the answers

-19.78 is what type of number?

<p>Rational</p> Signup and view all the answers

-√3/5 + 10.8 is what type of number?

<p>Irrational</p> Signup and view all the answers

-7.832198653... is what type of number?

<p>Irrational</p> Signup and view all the answers

-0.8662866239... is what type of number?

<p>Irrational</p> Signup and view all the answers

In $3√13$, what is the term called 13?

<p>Radicand</p> Signup and view all the answers

In $3√13$, what is the term called 3?

<p>Index</p> Signup and view all the answers

What is the expression $3√13$ called?

<p>Radical</p> Signup and view all the answers

0.225 equals 9/40.

<p>True (A)</p> Signup and view all the answers

-0.6 equals -4/7.

<p>False (B)</p> Signup and view all the answers

0.8 equals 8/10.

<p>False (B)</p> Signup and view all the answers

-3.143 equals -3140/999.

<p>True (A)</p> Signup and view all the answers

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Study Notes

Rational and Irrational Numbers

  • Rational Number: Can be expressed as a quotient of two integers; examples include terminating or repeating decimals.
  • Irrational Number: Cannot be expressed as a quotient of two integers; characterized by nonterminating, nonrepeating decimals.

Examples of Rational Numbers

  • 1,384: Classified as a rational number.
  • 0: Considered a rational number since it can be expressed as 0/1.
  • -19.78: Also a rational number, expressible as -1978/100.

Examples of Irrational Numbers

  • Ï€ (pi): A well-known irrational number not expressible as a simple fraction.
  • -0.28764...: An example of an irrational number with a nonterminating decimal.
  • -√3/5 + 10.8: Results in an irrational number.
  • -7.832198653... and -0.8662866239...: Both are classified as irrational due to their nonrepeating, nonterminating nature.

Radicals and Their Components

  • In the expression ³√13:
    • Radicand: The number inside the radical, here it is 13.
    • Index: The number that indicates the root being taken, here it is 3.
    • Radical: The entire expression (³√13) is known as a radical.

True or False Statements About Rational Numbers

  • True: 0.225 equals 9/40, confirming its rationality.
  • False: -0.6 equals -4/7; this statement is incorrect.
  • False: 0.8 is not equal to 8/10; this statement is false.
  • True: -3.143 equals -3140/999, verifying its classification as a rational number.

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