Repeating Decimals
What is 0.5555555.... as a fraction?
5/9
Is 1/2 rational or irrational?
Rational
0.25
Rational
Convert 0.75 to a fraction.
3/4
Is √225 a rational number?
Yes, √225 = 15
What is 2.34444444... as a fraction
2 31/90
Is 8.2759934562966... rational or irrational?
Irrational
√2
Irrational
Is 0.57575757... a rational number? Explain.
Yes, it's a repeating decimal and equals 57/99.
Is √20 a rational number?
No, it cannot be simplified to a whole number.
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, √100, √125?
√125 is irrational (√36 = 6, √100 = 10)
What is 1.26565656565... as a fraction
1 263/990
Is root(3)(-1000/49) rational or irrational?
irrational; 49 is a perfect cube
-4/9
Rational
What kind of number is 5.212121...?
Rational (it's a repeating decimal)
Solve:
2x^2+18=1268
x = 25, -25
What is 1.623333333333... as a fraction?
1 561/900
Is sqrt256/4 a rational number?
Yes, it equals 4.
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 and it cannot be written as a fraction.
Solve:
5x^3-14=3631
x = 9