Numbers help us in counting, measuring, and labeling. The numbers derived from the basic ten digits in arithmetic have been classified into a number of types depending upon their properties or the purpose they serve. Here let us talk about how rational numbers are different from irrational numbers for a subject like mathematics which is widely known for its logical accuracy; how is it that we have a whole stream of numbers which are curiously called rational and irrational.
Before proceeding towards the difference between rational and irrational numbers, let us refresh the different types of numbers we know, like the integers, digits, numeral, natural numbers, whole numbers, fractional numbers, real numbers, etc. Math worksheets are a good way to strengthen the concept of numbers as they offer a lot of practice problems to the students. Many websites these days offer interactive worksheets which are easy to download. Cuemath is one of them, which provides worksheets on a variety of math topics and also based on age groups. Like 6th-grade math worksheets are specifically designed to keep the sixth-grade students in mind.
Any positive and negative whole numbers are called integers, also known as the natural or counting numbers. The whole numbers are again the natural numbers itself as well as the zero. Fractional numbers are the numbers expressed as part of the whole; they have a numerator and denominator separated by a fraction bar. Rational numbers are those numbers that can be expressed as a fraction, where there are integers in the numerator and the denominator. And there can be two different fractions referring to the same rational number like 5/4 = 10/8
Like 0.25 = 1/4 is a rational number
All whole numbers can also be called rational numbers since they can be written as the number divided by 1. Like 4 is a rational number as it can be written as 4/1. In simple terms, it is a number that can be formed by dividing two integers, where integers are those numbers that possess no fractional part. Also, the word rational is derived from the word ratio.
There can be negative rational numbers, too, like -1/4, -3/4.
Coming to irrational numbers, those numbers cannot be expressed as the ratio of two integers like the square root of 2. The square root of 2 is a very curious number, for if we have a right-angled triangle with both its length and base of 1 unit, then the hypotenuse of such a right-angled triangle would be the square root of 2. Now we can never have the exact value of the square root of 2 expressed in decimals. Let us consider another celebrity irrational number called “pi” which is an amazing number for it is this one number that connects the length of the radius of a circle to its circumference or area. This number pi can be easily expressed as a fraction which is 22/7 but when tried to convert into a decimal, the digits after the decimal point are unending like 22/7= 3.1415926535897932…… Thanks to the universal fan following of the number “pi” there are many contests to see who can recite the value of “pi” to a maximum number of decimal places.
Keep in mind that pi multiplied by pi again gives an irrational number, but when the square root of two is multiplied with itself, we get a rational number that is two. Thus multiplying irrational numbers can result in both rational and irrational numbers.
