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
. 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
, a ratio of two integers.
4. 1/3 is a rational number as it can be represented as a fraction
, 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
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
, a ratio of two integers.
9. 1 is a natural number and also a rational number because it can be expressed as
meeting the criteria for rational numbers.