Before we consider the given number, let's recall the various types of numbers.
Rational Number: A number is a rational number if it can be written in the form ab, where a and b are both integers and b≠0.
Integer: A number is an integer if it is a positive or negative counting number (or zero). All integers are also rational numbers because any number can be written as a division by one, a1.
Whole Number: A number is a whole number if it is a non-negative counting number. All whole numbers are also integers and rational numbers.
Natural Number: A number is a natural number if it is a positive counting number. All natural numbers are also whole numbers, integers, and rational numbers.
Irrational Number: An irrational number is a number that cannot be written in the form of a rational number. These are recognized as being non-repeating, infinite decimals.
Now, let's try to categorize the given number using these definitions.
-2.324
We will rewrite the given decimal as fraction.
Since - 2.324 can be rewritten as a fraction in which both the numerator and the denominator are integers, it is a rational number. What is more, the fraction cannot be reduced, therefore the number does not belong to any other subset.
b
Let's categorize the given number using the definitions from Part A. We will also split the number 46 into factors so that is is clear whether or not the square root can be simplified.
sqrt(46)=sqrt(2*23)
Since none of the factors of the radicand are perfect squares, this square root cannot be simplified. We can, however, use a calculator to find its exact value.
sqrt(46)=6.78232...
Because the decimal part is infinite with non-repeating digits, sqrt(46) is an irrational number.
