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Questions and Answers
What is a rational number?
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?
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?
Is 1384 a rational number?
Yes
Is π a rational number?
Is π a rational number?
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-0.28764... is what type of number?
-0.28764... is what type of number?
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Is 0 a rational number?
Is 0 a rational number?
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-19.78 is what type of number?
-19.78 is what type of number?
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-√3/5 + 10.8 is what type of number?
-√3/5 + 10.8 is what type of number?
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-7.832198653... is what type of number?
-7.832198653... is what type of number?
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-0.8662866239... is what type of number?
-0.8662866239... is what type of number?
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In $3√13$, what is the term called 13?
In $3√13$, what is the term called 13?
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In $3√13$, what is the term called 3?
In $3√13$, what is the term called 3?
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What is the expression $3√13$ called?
What is the expression $3√13$ called?
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0.225 equals 9/40.
0.225 equals 9/40.
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-0.6 equals -4/7.
-0.6 equals -4/7.
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0.8 equals 8/10.
0.8 equals 8/10.
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-3.143 equals -3140/999.
-3.143 equals -3140/999.
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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
- π (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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