Classify all the following numbers as natural, whole. Integer rational, or irrational List all that apply. b. 0
Answers
Answer:
Natural numbers are the numbers
1
,
2
,
3
,
...
or the numbers
0
,
1
,
2
,
3
,
...
according to whose definition you choose. So
0
may be considered a natural number or not.
Whole numbers are the numbers
0
,
1
,
2
,
3
,
...
Integers include negative numbers, but not fractions. So the integers are:
0
,
1
,
−
1
,
2
,
−
2
,
3
,
−
3
,
...
Rational numbers are any number that can be expressed as
p
q
where
p
and
q
are integers and
q
≠
0
. So
5
,
12.42
,
−
17
3
and
0
are rational numbers.
There are infinitely many rational numbers, but they do not form a continuous line. The continuous line of numbers is called the real number line. It includes all the previous numbers we have mentioned, but also numbers like
√
2
,
π
and
e
, which are not rational. Some real numbers - such as
√
2
- are the roots of polynomials with integer coefficients. These are known as algebraic numbers.
Irrational numbers are any real numbers that are not rational. So 0
is not an irrational number