Rational Numbers The real number system consists of rational and irrational numbers Rational numbers can be expressed in fractional form where a the numerator and b the denominator are both integers and b 0 ID: 322896
Download Presentation The PPT/PDF document "Rational & Irrational Numbers" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Rational & Irrational NumbersSlide2
Rational Numbers
The
real number system consists of rational and irrational numbers. Rational numbers can be expressed in fractional form, , where a (the numerator) and b (the denominator) are both integers and b = 0. This means that the decimal form of the number either terminates or repeats. Counting numbers, whole numbers, integers, and non-integers are all rational numbers.
a
bSlide3
Counting
numbers {1, 2, 3, 4, 5, 6, …} Whole numbers consist of the counting numbers and zero. {0, 1, 2, 3, 4, 5, …} Integers consist of the counting numbers, their opposites, and zero.
{…, -3, -2, -1, 0, 1, 2, 3, …} Slide4
Non-integers
consist of fractions that can be written as terminating or repeating decimals.A terminating decimal comes to a complete stop.A repeating decimal continues the same digit or block of digits forever. 2
3
7
5.25
1
3
0.6
-9.261Slide5
Irrational Numbers
Irrational numbers are numbers that cannot be written as a ratio of two integers. Irrational numbers are non-repeating and non-terminating decimals because the decimal form of the number never ends and never repeats. The most common irrational number is pi (п). The value of
п is 3.141592654… Slide6
Example 1
Tell whether each real number is rational or irrational.
-23.75 rational decimal terminates4.750918362… irrational decimal does not terminate59√15 irrational decimal form does not terminate
rational
number is in fraction formSlide7
Rational and Irrational Numbers
Combining
Rationals
and Irrationals
Addition and subtraction of
any number
to an irrational number gives another irrational
number
Examples of irrationalsSlide8
Rational and Irrational Numbers
Combining
Rationals
and Irrationals
Multiplication and division of an irrational number by another irrational can often lead to a rational number
. (but not always)
Examples of Rationals
21
26
8
1
-13Slide9
Rational and Irrational Numbers
Combining
Rationals
and Irrationals
Determine whether the following are rational or irrational.
(a) 0.73 (b)
(c) 0.666…. (d) 3.142 (e)
(f) (g)
(h) (i)
(j)
(j) (k)
(l)
irrational
rational
rational
rational
irrational
irrational
irrational
rational
rational
irrational
irrational
rational
rational