Questions: What is the narrowest definition of the number 1/20? Natural Number Whole Number Integer Rational Number Irrational Number

Transcript text: What is the narrowest definition of the number $\frac{1}{20} ?$ Natural Number Whole Number Integer Rational Number Irrational Number

Solution

Solution Steps

To determine the narrowest definition of the number $\frac{1}{20}$, we need to classify it according to the types of numbers. A rational number is any number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $q \neq 0$. Since $\frac{1}{20}$ is a fraction of two integers, it is a rational number. It is not a natural number, whole number, or integer because those are typically non-fractional numbers. It is also not an irrational number, as irrational numbers cannot be expressed as a simple fraction.

Step 1: Classifying the Number

The number $\frac{1}{20}$ can be expressed as a decimal, which is $0.05$. To classify this number, we need to determine its type based on the definitions of various number sets.

Step 2: Determining the Type

Natural Numbers: These are positive integers starting from $1$ (i.e., $1, 2, 3, \ldots$). Since $0.05$ is not a positive integer, it is not a natural number.
Whole Numbers: These include all natural numbers and $0$ (i.e., $0, 1, 2, 3, \ldots$). Again, $0.05$ is not a whole number.
Integers: These are whole numbers that can be positive, negative, or zero (i.e., $\ldots, -2, -1, 0, 1, 2, \ldots$). Since $0.05$ is not an integer, it does not belong to this set.
Rational Numbers: These are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Since $\frac{1}{20}$ can be expressed as $\frac{1}{20}$ (where $1$ and $20$ are integers), it is a rational number.
Irrational Numbers: These cannot be expressed as a simple fraction. Since $0.05$ can be expressed as $\frac{1}{20}$, it is not an irrational number.