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˚le all number sets to which the given numbers belong.

4.7
a) Natural
b) Whole
c) Integer
d) Rational

√36
a) Natural
b) Whole
c) Integer
d) Rational

0
a) Natural
b) Whole
c) Integer
d) Rational

1/3
a) Natural
b) Whole
c) Integer
d) Rational

√10
a) Whole
b) Rational
c) Irrational

0.333...
a) Whole
b) Rational
c) Irrational

√12
a) Natural
b) Integer
c) Rational
d) Irrational

-1
a) Rational
b) Integer

1
a) Natural
b) Rational

User PierreD
by
7.7k points

1 Answer

2 votes

Final Answer:

1. 4.7: d) Rational

2. √36: b) Whole, c) Integer, d) Rational

Step-by-step explanation:

1. 4.7 is a rational number as it can be expressed as a fraction in the form of
\( (47)/(10) \). Rational numbers can be written as fractions where the numerator and denominator are integers and the denominator is not zero.

2. √36 equals 6, which is both a whole number and an integer. Whole numbers are non-negative integers (0, 1, 2, 3, ...) and integers include both positive and negative whole numbers (-3, -2, -1, 0, 1, 2, 3, ...). Both classifications apply to √36, making it a whole number and an integer, and since it's the square root of a perfect square, it's also rational.

3. 0 is a natural, whole, integer, and rational number. It is a natural number because it's a counting number, a whole number as it is non-negative, an integer since it's within the set of integers, and a rational number since it can be expressed as
\( (0)/(1) \), a ratio of two integers.

4. 1/3 is a rational number as it can be represented as a fraction
\( (1)/(3) \), where both the numerator and denominator are integers, and the denominator is not zero, meeting the criteria for rational numbers.

5. √10 is an irrational number because it cannot be expressed as a fraction of two integers. It is a non-repeating and non-terminating decimal.

6. 0.333... is a rational number because it can be expressed as
\( (1)/(3) \), a fraction of two integers.

7. √12 is an irrational number because it cannot be simplified to a fraction. It's a non-repeating, non-terminating decimal.

8. -1 is an integer but also a rational number since it can be expressed as
\( (-1)/(1) \), a ratio of two integers.

9. 1 is a natural number and also a rational number because it can be expressed as
\( (1)/(1) \), meeting the criteria for rational numbers.

User Gkuzmin
by
8.2k points