Definitions
What is a rational number?
A number that can be written as a fraction.
Is 1/2 rational or irrational?
Rational
0.25
Rational
Convert 0.75 to a fraction.
3/4
Is √25 a rational number?
Yes, √25 = 5
What is an irrational number?
A number that cannot be written as a fraction and has a non-repeating, non-terminating decimal.
Is 3.1415926... (non-repeating) rational or irrational?
Irrational
√2
Irrational
Is 0.333... a rational number? Explain.
Yes, it's a repeating decimal and equals 1/3.
Is √20 a rational number?
No, it cannot be simplified to a whole number.
True or False: All whole numbers are rational.
True. Whole numbers can be written as fractions (e.g., 4 = 4/1).
Is √16 rational or irrational?
Rational (√16 = 4)
-4/9
Rational
What kind of number is 5.212121...?
Rational (it's a repeating decimal)
What is the square root of 81?
9
Name two examples of irrational numbers.
Answers vary.
√2 or π
Is -7 a rational number?
Yes, it can be written as -7/1.
2.71828...
Irrational (this is the number e)
Why is 0.1010010001... irrational?
It has no repeating pattern, so it’s non-repeating and non-terminating.
Is √3 a rational number? Why or why not?
No, because it cannot be written as a fraction.
Explain the difference between a repeating decimal and a non-repeating decimal.
A repeating decimal has digits that repeat in a pattern (e.g., 0.333…), while a non-repeating decimal goes on forever without a pattern (e.g., π).
Is π/2 rational or irrational?
Irrational (π is irrational, and dividing it by a rational number keeps it irrational).
√49
Rational (√49 = 7)
A student says that 0.676776777... is a rational number. Is the student correct? Explain why or why not.
No, the student is incorrect. The decimal 0.676776777... does not have a repeating pattern—it adds one more 7 each time. Since the digits do not repeat in a predictable way, it is non-repeating and non-terminating, which makes it irrational.
Which of these is irrational: √36, √18, √100?
√18 is irrational (√36 = 6, √100 = 10)