Definition: A rational number is any number that can be written as a fraction of two integers with a nonzero denominator, including terminating and repeating decimals.
What is a rational number?
A number is rational if it equals a/b, where a and b are integers and b is not 0. Rational comes from ratio.
Which numbers qualify?
- Integers, like 7 = 7/1 and -3 = -3/1
- Fractions, like 5/8
- Terminating decimals, like 0.375 = 375/1000 = 3/8
- Repeating decimals, like 0.666… = 2/3
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For 7/11, long division gives 0.636363…, which repeats forever. Every rational number’s decimal either stops or repeats.
What is not rational?
Square roots of non-perfect squares, like the square root of 2, and pi. Their decimals never repeat.
How do you compare them?
Convert to decimals or common denominators. Compare -3/4 and -5/7: the decimals are -0.75 and about -0.714, so -5/7 is greater.
What is a common mistake?
Thinking a long decimal is irrational. The decimal 0.142857142857… is rational, equal to 1/7.