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.
sqrt(10.24)
It may seem difficult at first to simplify the square root of 10.24. However, let's look at this number as though it was not a decimal value (just for a little while). The number 1024 is actually a perfect square. We will show how to find its root below.
Now that we know that sqrt(1024) = 32, we can use this to find sqrt(10.24). When we multiply decimals, we add the number of decimal places from each factor to find the number of decimals in the product.
3.2_(1 decimal)*3.2_(1decimal)&=10.24_(2 decimal places) [2em]
sqrt(10.24)&=3.2
The number 3.2 has a finite number of digits after the decimal so it can be rewritten in the form ab where a and b are integers and b≠0.
