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Making Sense of Rational and Irrational Numbers

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Objectives: Identify number sets. Write decimals as fractions. Write fractions as decimals. The set of real numbers is all numbers that can be written on a number line. – PowerPoint PPT presentation

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Title: Making Sense of Rational and Irrational Numbers


1
Making Sense of Rational and Irrational Numbers
  • Objectives Identify number sets.
  • Write decimals as fractions.
  • Write fractions as decimals.

2
The set of real numbers is all numbers that can
be written on a number line. It consists of the
set of rational numbers and the set of irrational
numbers.
3
Recall that rational numbers can be written as
the quotient of two integers (a fraction) or as
either terminating or repeating decimals.
4 5
23
3 3.8
0.6
1.44 1.2
4
Rational Numbers
Natural Numbers -
Natural counting numbers.
1, 2, 3, 4
Whole Numbers -
Natural counting numbers and zero.
0, 1, 2, 3
Integers -
Whole numbers and their opposites.
-3, -2, -1, 0, 1, 2, 3
Rational Numbers -
Integers, fractions, and decimals.
-0.76, -6/13, 0.08, 2/3
Ex
5
Biologists classify animals based on shared
characteristics. The horned lizard is an animal,
a reptile, a lizard, and a gecko. Rational
Numbers are classified this way as well!
You already know that some numbers can be
classified as whole numbers, integers, or
rational numbers. The number 2 is a whole number,
an integer, and a rational number. It is also a
real number.
Animal
Reptile
Lizard
Gecko
6
Venn Diagram Naturals, Wholes, Integers,
Rationals
Real Numbers
Rationals
Integers
Wholes
Naturals
7
Name all the sets of numbers to which the
given number belongs. Circle the most specific
set.
Integers
, Rationals
Rationals
, Integers
, Rationals
Naturals
, Wholes
, Integers
, Rationals
Wholes
Rationals
8
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9
Reminder
  • Real numbers are all the positive, negative,
    fraction, and decimal numbers you have heard of.
  • They are also called Rational Numbers.
  • IRRATIONAL NUMBERS are usually decimals that do
    not terminate or repeat. They go on forever.
  • Examples p

10
Identify each root as rational or irrational.
11
Decimal to Fraction A skill you will need for
this unit!
  • To change a decimal to a fraction, take the place
    value and reduce!
  • 0.5 means 5 tenths, so 5/10.
  • Now reduce 5/10 ½
  • 0.5 1/2

12
Converting Fractions and Decimals
Fraction
Decimal
To change a fraction to a decimal, take the top
divided by the bottom, or numerator divided by
the denominator.
13
Complete the table.
Fraction
Decimal
14
Repeating Decimals
Fraction
Decimal
Every rational number (fraction) either
terminates or repeats when written as a decimal.
15
Repeating Decimals
Fraction
Decimal
16
Repeating Decimals
Fraction
Decimal
17
Thankyou
We shall continue with representing Rational and
Irrational Numbers on the Number Line in
forthcoming sessions
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