Section 1 - Rational and irrational numbers Flashcards
What is a rational number?
A number that can be expressed as the quotient or fraction of two integers.
True or False: All integers are rational numbers.
True
Provide an example of an irrational number.
√2 or π
Fill in the blank: A rational number can be written as a fraction a/b where a and b are _____ and b ≠ 0.
integers
What is the decimal representation of a rational number?
It either terminates or repeats.
True or False: The number 0.333… is a rational number.
True
What type of number is √9?
Rational number
Is the number 5.12 a rational number?
Yes
What is an example of a number that is neither rational nor irrational?
None, all numbers are either rational or irrational.
Fill in the blank: The square root of a non-perfect square is _____ .
irrational
True or False: The number -2 is an irrational number.
False
What is the sum of two rational numbers?
It is always a rational number.
What is the product of a rational number and an irrational number?
It is always an irrational number.
Provide a definition for an irrational number.
A number that cannot be expressed as a fraction of two integers.
True or False: The number 0.1010010001… is a rational number.
False
What is the difference between rational and irrational numbers?
Rational numbers can be expressed as fractions; irrational numbers cannot.
Fill in the blank: The number π is an example of a _____ number.
irrational
Is the number 3.75 a rational number?
Yes
What does it mean for a decimal to terminate?
It ends after a finite number of digits.
True or False: The number 2/3 is a rational number.
True
What is the square root of 16?
4, which is a rational number.
Fill in the blank: The sum of two irrational numbers can be _____ .
rational or irrational
What type of number is 0?
Rational number
Is the number 5.142857142857… a rational number?
Yes, it has a repeating decimal.
What is the product of two rational numbers?
It is always a rational number.
True or False: The number √3 is a rational number.
False
What is the decimal representation of the rational number 1/4?
0.25
Fill in the blank: The number 0.5 can be expressed as a fraction _____ .
1/2
What happens when you divide a non-zero rational number by an irrational number?
The result is irrational.
Is -√5 a rational number?
No, it is irrational.
What is the sum of 1/2 and 1/3?
5/6, which is rational.
True or False: The number 7.0 is an irrational number.
False
