NOTES-­‐ RATIONAL NUMBERS Date ___________________ RATIONAL NUMBERS are numbers that can be expressed as fractions. This includes natural numbers, whole numbers and integers. If a number is not rational, it is an IRRATIONAL NUMBER. Natural numbers (counting numbers) {1, 2, 3, 4…} Zero is NOT included in the natural numbers. Whole numbers  All natural numbers and zero. {0, 1, 2, 3, 4…} Integers  All whole numbers and their opposites. {… -­‐3, -­‐2, -­‐1, 0, 1, 2, 3…} Rational numbers as a fraction Any rational number can be written as a ratio of two numbers, in the form where a and b are integers and b is not zero. Rational numbers as a whole number Any integer can be written as a rational number! How? 43 -­‐12 Rational numbers as decimals Terminating decimals have an “end.” 0.7 0.26 1.203 2.93 Terminating decimals ARE ALWAYS rational numbers Repeating decimals are decimals that repeat with no end. 0.333…=
5.81666…=
0.141414…=
Repeating decimals ARE ALWAYS rational numbers. Non-­terminating, non-­repeating decimals ARE NOT rational numbers. π = 3.14159265… 0.5480390857… Testing whether a decimal is terminating or repeating: EXAMPLE 1: Write 5/8 as a decimal. EXAMPLE 2: Write 7/12 as a decimal. Testing Square Roots: means the number that multiplied by itself gives you 81. Since 9 9 = 81, = 9. is a rational number. means the number that multiplied by itself gives you 40.  too low  too high Since no whole number works, is NOT a rational number.