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Number Families
The Natural Numbers are
The Whole Numbers are
The Integers are
The Rational Numbers are
The Irrational Numbers are
The Real Numbers are
The Natural Numbers are also called the
{ 1, 2, 3, … }
Counting Numbers, because they’re the
numbers we usually use to count stuff.
The Whole Numbers are made from the
{ 0, 1, 2, 3, … }
Natural Numbers plus the very special
number 0 thrown in, too.
The Integers are all of the Whole Numbers
{ …, -3, -2, -1, 0, 1, 2, 3, … }
plus the opposites, the negative versions
of the Natural Numbers, too.
1
7
For
example,
and
−
All the numbers that can be made by
2
3
forming a fraction with two integers, All terminating decimals are also rationals,
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑜𝑛 𝑡𝑜𝑝
like 0.5 and –1.4399832
that is, the pattern
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑜𝑛 𝑏𝑜𝑡𝑡𝑜𝑚
All repeating decimals are also rationals,
(But you can’t put 0 on bottom.)
like 2.34343434… and −7.148̅
These include the weird numbers like
square roots that don’t come out evenly,
The ones that cannot be expressed
like √2 and √3 (but not √4, who’s exactly
as Rational Numbers
nice 2). And also 𝜋, the “pi” in geometry.
And all non-terminating, non-repeating
decimals, like 1.02002000200002
All of the Rational Numbers and all of The Number Line is a family photo of the
the Irrational Numbers taken
Real Numbers. Each point represents one
together.
particular real number.
more on the other side > > > > >
NumberFamilies.docx
6/27/2014 9:11 AM - D.R.S.
Many Numbers belong to More Than One Family
A Natural Number, such as 3… ... is also a member of the Whole Number family,
and is also a member of the Integer family,
and is also a member of the Rational Number family
3
because 3 has another name, , which fits into the Rationals.
1
A Whole Number, such as 0… … is also a member of the Integer family,
and is also a member of the Rational Number family
0
because 0 has another name, , which fits into the Rationals.
1
An Integer, such as –3… … is also a member of the Rational Number family
−3
because – 3 has another name, , which fits into the Rationals.
1
All of the Natural Numbers and ...are also members of the Real Number family,
all of the Whole Numbers and because they all have homes on the number line.
all of the Integers and Every one of them can be located at some point on the number line.
all of the Rational Numbers and
all of the Irrational Numbers…
Beware of Numbers in Disguise – here are some examples
√25 is not an Irrational Number … … because he’s just another name for 5.
√25 is really a Natural Number (and thus also Whole, Integer, and
Rational)
24
is a Natural Number … because he’s just another name for 4,
6
24
therefore belongs to the Natural and Whole and Integer and Rational
6
families.
1.02002000200002… …even though it’s a decimal and it sort of repeats, the repetition is a
is an Irrational Number… pattern, not a repetition of the same exact digits over and over.
But 1.020202020202… …because it’s genuinely a repeating decimal; the digits 02 repeat over
is a Rational Number and over, forever and ever.
NumberFamilies.docx
6/27/2014 9:11 AM - D.R.S.