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.
0.57
Note that the given expression is an infinite repeating decimal.
0.57=0.575757...
All repeating decimals are rational numbers since they can be rewritten as a fraction of form ab, where a and b are integers and b≠0. Therefore, we can classify the number as a rational number.
Extra
Writing 0.57 as a fraction
To demonstrate that 0.57 is a rational number, we will rewrite it in the form ab, where a and b are integers and b≠0.
The expression 0.57 is the same as 0.575757... where 57 repeats infinitely many times. Let x be the number.
x=0.575757...
By multiplying both sides of the equation by 100, we create a new equivalent equation.
The fraction 1933 is equivalent to 0.57. Thus, 0.57 fulfills the definition of a rational number, because it can be expressed as a fraction in the form ab, where a and b are integers and b≠0.
