Rational and
irrational numbers are two very essential types of numbers in mathematics. In
most of the mathematics papers, a number is given and the students are asked to
get an idea whether it is a rational number or an irrational number. The
students can easily get an idea about the rational and irrational numbers by
getting an idea about the difference between rational and irrational numbers. Here, we will try to explain
rational and irrational numbers with the help of examples.
Table of rational and irrational numbers
If you don’t
have enough idea about the table of rational and irrational numbers, it is
almost impossible for you to differentiate the rational numbers from the
irrational numbers. The main points of this table are given below;
1)
All
the perfect squares are rational numbers i.e 16 is a rational number. Its reason
is that 16 is a perfect square of 4.
2)
All
the surds are irrational numbers. √3 is an irrational number. Its reason is
that √3 is not a perfect square of any real number.
3)
All
the terminating decimals are rational numbers. Terminating decimals are those
decimals which stop the division process after the point. For example, 2.55 is a
terminating decimal.
4)
All
the non-terminating and non-repeating decimals are irrational numbers. Non-terminating
and non-repeating decimals are those decimals which repeat the same numbers
after the point. For example, 2.523567839402…. is a non-terminating and
non-repeating decimal.
5)
All
the repeating decimals are rational numbers. The numbers that repeat the same
words are repeating decimals. For example, 2.55555…. is an essential example of repeating decimals.
Is √2 is a rational or irrational number?
After
understanding the difference between rational and irrational numbers, we are in
a position to get a clear idea of which number is rational and which is
irrational. If we take an overview of √2, we can get an idea that √2 is a surd.
From the table of difference between the rational and irrational numbers, we
can get an idea that all the surds are irrational numbers. As √2 is a surd,
therefore, we can say that √2 is an irrational number.
Is √4 is a rational or irrational number?
√4 is a
perfect square. After solving it, we can get its answer as 2. From the table of
rational and irrational numbers, we also get an idea that all the perfect
squares are rational numbers. As √4 is a perfect square of 2, therefore, we can
say that √4 is a rational number.
Is 9/7 is a rational number or an irrational number?
Before getting
an idea either 9/7 is a rational number or an irrational number, we have to
divide it. After dividing 9/7, we get the answer 1.285714….. It means that it
is non-terminating and non-repeating decimal. From the table of rational and
irrational numbers, we also know that all the non-terminating non-repeating decimals
are irrational numbers. Therefore, we can also say that 9/7 is also an
irrational number.
Is 3/2 is a rational number or an irrational number?
Like 9/7, if
we want to get an idea about 3/2, it is also necessary for us to divide it.
After dividing 3/2, we get the answer 1.5.1.5 is a terminating decimal. From
the table of rational and irrational numbers, we know that all the terminating
decimals are also rational numbers. Therefore, we can say that 3/2 is a
rational number.
Is 2/3 is a rational number or an irrational number?
After
dividing 2/3, we get the answer 0.666666…… It means that it is non-terminating
and repeating decimal. From the table of rational and irrational numbers, it is
clear that all the non-terminating and repeating decimals are irrational
numbers. Therefore, we can say that 2/3 is a rational number.
Conclusion
To sum up,
we can say that there are two things to differentiate the rational numbers from
the irrational numbers. First of all, we should take an overview of the table
of rational and irrational numbers. This table will provide us with a clear
idea about rational and irrational numbers. Secondly, we should get an idea
about the nature of the given numbers. After comparing these numbers with this
table, we will be in a better position to differentiate between these two
numbers.
