Sandra Luna McCune - McGraw-Hill Education Algebra I Review and Workbook

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The real numbers consist of the rational numbers and the irrational numbers. A rational number is a number that can be expressed as a quotient of an integer divided by a nonzero integer. (The integers are the numbers , 3, 2, 1, 0, 1, 2, 3, .) The decimal representations of rational numbers terminate or repeat.

The irrational numbers are numbers that cannot be expressed as the quotient of two integers. Their decimal representations neither terminate nor repeat. Frequently, real numbers are called signed numbers because they are positive, negative, or zero. EXAMPLE The three dots indicate that the pattern continues in the same manner without end. The bar above 14 means that a block of digits continues to repeat without end. The number is the ratio of the circumference of a circle to its diameter.

EXERCISE 1.1

9.22 0.454554555 0.111 100.121212 0.025 0.333 101,001,000 0.010010001 0.454545 A letter that is used to represent a number is a variable. If n is a positive integer, an nth root of x is a number that when used as a factor n times gives x, the numbers nth power. The notation is a radical. It indicates an nth root of the number x. The number n is the index, and x is the radicand. (Even roots of negative numbers are not real numbers.) If n is a positive odd integer and x is any real number, then indicates the real nth root of x. (Even roots of negative numbers are not real numbers.) If n is a positive odd integer and x is any real number, then indicates the real nth root of x.

A number that is an exact nth power of another number is a perfect nth power. Roots of perfect nth powers are rational numbers, while roots that cannot be determined exactly are irrational numbers. Decimal representations of irrational numbers are given as approximations. For example, . EXAMPLE EXERCISE 1.2