Algebra 1 Common Core Student Edition, Grade 8-9

Think
What clues can you
use to classify real
numbers?
Look for negative signs,
fractions, decimals that
do or do not terminate
or repeat, and radicands
that are not perfect
squares.

A rational number is any number that you can write in the form |, where a and b are

integers and b + 0. A rational number in decimal form is either a terminating decimal^

such as 5.45 or a repeating decimal such as 0.41666..., which you can write as 0.416.

Each graph below shows a subset of the rational numbers on a number line.

Natural numbers

Whole numbers

Integers

{1 ,2,3,...}

{0, 1, 2, 3 ,... }

{...-2,-1 ,0 , 1,2,3,...}

H h

2 -1

H 1-

-1 1

-2-1 01 23

An irrational number cannot be represented as the quotient of two integers. In

decimal form, irrational numbers do not terminate or repeat. Here are some examples.

0.1010010001... 7 T = 3.14159265 ...

Some square roots are rational numbers and some are irrational numbers. If a whole

number is not a perfect square, its square root is irrational.

Rational Vi = 2 V 25 = 5

Irrational V 3 = 1,73205080... VTo = 3.16227766 ...

Rational numbers and irrational numbers form the set of real numbers.

^ESSSSDCl assi f y i n g Real N u m b er s

To which subsets of the real numbers does each number belong?

Q 1 5 natural numbers, whole numbers, integers, rational numbers

_

| J — 1 .4 5 8 3 rational numbers (since - 1. 4 5 8 3 is a term inating decimal)

0 V 5 7 irrational numbers (since 57 is not a perfect square)

G o t It? 3. To which subsets of the real numbers does each number belong?

a. V9 b. ^ c. - 0 .4 5 d. V l2

Co n cep t Su m m a r y Real Number s

Real Numbers

Rat i o n al

Numbers Integers

-2 -3

3

10

0.3 5

Vfr25 -v ie

Whole

Numbers

0

Natural

Numbers

V25

i »

Irrational

Numbers

VTo - V m

0. 1010010001 ...

7 T

18 Chapter 1 Foundations for Algebra