6th Grade Math Textbook, Fundamentals

Lesson 10-4 for exercise sets. Chapter 10 279

Practice & Activities

 are numbers such as that cannot be expressed

as quotients of two integers, , where b 0. When an irrational number

is expressed in decimal form, the digits do not terminate and do not repeat.

• The numbers 0.01011011101111... and 12.34567819...are examples
  of irrational numbers.


• The square root of any whole number that is not a perfect square is
  an irrational number.


• The number pi, which is symbolized by the Greek letter , is an
  example of an irrational number. Pi is the relationship between the
  circumference (C) of any circle and its diameter (d).

So is an irrational number because it is the square root

of a whole number that is not a perfect square.

44

44

Irrational numbers

a

b

Real Numbers

Irrational Numbers Rational Numbers

Integers

Whole Numbers

Natural

Numbers

Which of the following numbers is irrational? Explain why.

Number Type and Explanation

Irrational; 35 is not a perfect square.

Rational; is a quotient of two integers.

Rational; 100 is a perfect square and 10.

1.65 Rational; 1.65 is a terminating decimal.

 100  100

17

41

17

41

35

1

Remember:The set of rational

numbers includes natural

(counting) numbers, whole

numbers, integers, proper

fractions, improper fractions,

mixed numbers, terminating

decimals, repeating decimals,

and percents.

The set of rational numbers

and the set of irrational numbers

together make up the set

of .real numbers

Classify each number as rationalor irrational.

1. 
   
   
   
   2. 3.3.33 4.0.875
   
   
   
   

Identify the closest perfect squares. Find the square root to the nearest whole number.

9.Discuss and Write Find three irrational numbers between 7 and 8.

Explain how you found your answers. How many irrational numbers

are between 7 and 8?

67 80 6 19



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