Question

Zero is a rational number. If this is true then enter 1 and if it is false enter 0.

Answer 1

Hint: First of all, try to recall what rational and irrational numbers are and then try to figure out in which form 0 can be expressed.

Complete step-by-step answer:
In this question, we have to figure out if 0 is a rational number or not. Before proceeding with the question let us have a look at a few terms.


Real numbers: Real numbers are the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line. At the same time, the imaginary numbers are the un-real numbers, because we cannot express them in the number line and it is commonly used to represent a complex number. Examples are 6, 2.5, -9, pi etc.

Rational numbers: Rational numbers are the numbers which can be expressed as a fraction and also as positive numbers, negative numbers and zero. It can be written as $\dfrac{p}{q}$ , where q is not equal to zero. Also rational numbers are either terminating or repeating numbers. Examples are 8, $\dfrac{7}{8}$ , 5.25, 6.999999…., etc.

Irrational numbers: The numbers which are not a rational number are called irrational numbers. Irrational numbers can be written in decimals but not in fractions which means that it cannot be written as the ratio of two integers. In other words we can say that irrational numbers are non-terminating, not repeating numbers.

Irrational numbers have endless non-repeating digits after the decimal point. A few examples of irrational numbers are: $\sqrt{5}=2.23607.....,\sqrt{3}=1.73205080.......$, etc.
Now, let us consider our question.
Now as we know what rational and irrational numbers are, let us check what type of number ‘0’ is.

We know that 0 is a whole number and does not have any fractional part and can be written as $\dfrac{0}{1}$ that is in $\dfrac{p}{q}$ form, where q is not equal to zero like rational number. It is also a terminating number. Hence we have found out that 0 is a rational number. Hence we will enter 1.

Note: Students must note that all the natural numbers, whole numbers and integers are rational numbers. Also, it must be noted that irrational numbers can never be expressed exactly, as it has infinite digits, so we can only express it approximately like we express pie which is an irrational number with the value 3.14 which is only its approximate value.