Question

"Identify all sets to which the number belongs

3.8
a. integer
b. irrational
c.rational, integer, whole
d.rational, integer, whole, natural

5.075
a. integer
b. irrational
c.rational, integer, whole
d.rational, integer, whole, natural

Answer 1

The numbers 3.8 and 5.075 belong to the sets: rational, integer, whole, rational, integer, whole, respectively.

Step-by-step explanation:

The number 3.8 belongs to the following sets:

integer: The number 3.8 is not an integer because it has a decimal part.

irrational: The number 3.8 is not irrational because it can be expressed as a finite decimal.

rational, integer, whole: The number 3.8 is a rational number because it can be expressed as a fraction (19/5) and it is not an integer or a whole number.

rational, integer, whole, natural: The number 3.8 is not a natural number because it is not a positive whole number.

The number 5.075 belongs to the following sets:

integer: The number 5.075 is not an integer because it has a decimal part.

irrational: The number 5.075 is not irrational because it can be expressed as a finite decimal.

rational, integer, whole: The number 5.075 is a rational number because it can be expressed as a fraction (407/80) and it is not an integer or a whole number.

rational, integer, whole, natural: The number 5.075 is not a natural number because it is not a positive whole number.

Answer 2

The numbers 3.8a and 5.075a belong to the set of rational numbers. They do not belong to the sets of integer, whole, or natural numbers.

Step-by-step explanation:

The number 3.8a belongs to the following sets:

1. Rational numbers: A rational number is a number that can be expressed as a fraction, where both the numerator and the denominator are integers. Since 3.8a can be written as the fraction 38/10, it is a rational number.
2. Whole numbers: Whole numbers are non-negative integers. Since 3.8a is not an integer, it is not a whole number.

The number 5.075a belongs to the following sets:

1. Rational numbers: Similar to 3.8a, 5.075a can be expressed as the fraction 5075/1000, making it a rational number.
2. Whole numbers: Since 5.075a is not an integer, it is not a whole number.
3. Natural numbers: Natural numbers are positive integers. Since 5.075a is not an integer, it is not a natural number.