Rational and Irrational Numbers — Chapter Summary

A number that can be expressed

A number that can be expressed as a/b, where a and b are integers and b is not zero, is a rational number. Every integer and every decimal number is r

Irrational numbers are non

Irrational numbers are non-terminating, non-recurring decimals and cannot be written as p/q. Square roots, cube roots, and similar roots are irrationa

The set of real numbers

The set of real numbers is the union of rational numbers and irrational numbers, written as R = Q ∪ Q̄.

A terminating decimal ends after

A terminating decimal ends after a finite number of digits. A recurring decimal repeats one digit or a block of digits continuously. A mixed recurring

A rational number has a terminating

A rational number has a terminating decimal form when its denominator can be written as 2^m × 5^n, where m and n are whole numbers.