What type of number has non-repeating, infinite decimals?
Irrational number
Practice makes perfect
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.
Let's use these definitions to categorize our real number.
sqrt(101)
The square root cannot be simplified, but we can use a calculator to find its exact value.
sqrt(101)=10.049875...
Because the decimal part is infinite with non-repeating digits, sqrt(101) is an irrational number.
