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What Are Rational And Irrational Numbers?

Rational and irrational numbers

Rational and irrational numbers are taught in Grade 9 math. Pupils already learn rational numbers from the sixth grade, but irrational numbers are introduced in the ninth grade (in most schools). When I start teaching ninth graders, they seem very confused about these two types of numbers. Let’s take these two types one by one.

Rational numbers:

In the system of real numbers, the rational numbers are the fractions (mainly). Any number that can be written as “p/q”, where “p” and “q” are both integers and “q” is not equal to zero, is called the rational number. There is a “Q” letter symbol to denote them.

For example; 2/3 and -2/3 are both examples of a rational number.

But they are not limited to just fractions. All trailing (trailing) decimals and repeating decimals are in this category. For example; 2.5, – 2.5, 5.009 and repeating decimals like 0.3333… and 2.666… ​​fall under the symbol Q.

Also, all whole numbers can be changed to fractions by making one as the denominator; therefore, all integers such as -5, -4, -3, 0, 1, 2, 3 and so on fall into this category.

Therefore, rational numbers contain a variety of numbers in them. Below there are more examples of rational numbers.

0, 1, -1, 2, -2, 0.56, 3.125, 3/6, -5/2, 3.22222…., 0.99999….

Irrational numbers:

These are defined as non-repeating, non-terminating decimals. In other words, if a decimal does not end and the numbers after the decimals are not in a pattern, that number is a rational number. These types of numbers are obtained when the square root of a number (which is not a perfect square) is calculated.

For example; 3.013004751224… is an irrational number. Look at the pattern after the decimal is not in a pattern and no body can predict what comes after the last digit “4” and it’s also an endless decimal.

If we find the square root of the number “2” using the calculator, we find a decimal number which is an irrational number. Likewise, the square root of the number “3” falls into the same category. But be careful in the case of perfect squares such as “4”, because the square root of four is “2” which is a natural number and therefore a rational number but not an irrational number because four is a perfect square. Similarly, all other perfect squares like 16, 25, 36, 49, 64, 81, 100, 121, 144 and so on should be considered in their category.

Likewise, the square root of the next perfect square “9” is “3”, which is not an irrational.

I always ask my students to remember the irrational number because they are endless, non-repeating decimals and everything else is rational numbers.

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