Making Sense of Rational and Irrational Numbers

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Making Sense of Rational and Irrational Numbers

• Objectives Identify number sets.
• Write decimals as fractions.
• Write fractions as decimals.

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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.
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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
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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
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Venn Diagram Naturals, Wholes, Integers,
Rationals
Real Numbers
Rationals
Integers
Wholes
Naturals
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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
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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

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Identify each root as rational or irrational.
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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

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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.
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Complete the table.
Fraction
Decimal
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Repeating Decimals
Fraction
Decimal
Every rational number (fraction) either
terminates or repeats when written as a decimal.
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Repeating Decimals
Fraction
Decimal
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Repeating Decimals
Fraction
Decimal
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Thankyou
We shall continue with representing Rational and
Irrational Numbers on the Number Line in
forthcoming sessions