Question

0 is greater than every _______ integer.
(a) Negative
(b) Positive
(c) Rational
(d) Irrational

Answer 1

Hint:
Here, we need to fill the blank with the correct option. Here we will analyse the given statement. Then we will use examples to find the correct option to fill the blank and complete the statement.

Complete step by step solution:
We will use examples to find the correct option.
Let us take the negative integer \[ - 11\].
Comparing the negative integer \[ - 11\] with 0, we get the inequation
\[ \Rightarrow - 11 < 0\]
We can observe that 0 is greater than the negative integer \[ - 11\].
Similarly, 0 is greater than every negative integer.
Thus, option (a) is correct.
We will also check the other options.
Let us take the positive integer 15.
Comparing the positive integer 15 with 0, we get the inequation
\[ \Rightarrow 15 > 0\]
We can observe that 0 is lesser than the positive integer 15.
Similarly, 0 is lesser than every positive integer.
Thus, option (b) is incorrect.
Let us take the rational number \[\dfrac{7}{2}\].
Rewriting the rational number as a decimal, we get
\[ \Rightarrow \dfrac{7}{2} = 3.5\]
Comparing the rational number \[3.5\] with 0, we get the inequation
\[ \Rightarrow 3.5 > 0\]
We can observe that 0 is lesser than the rational number \[3.5\], that is \[\dfrac{7}{2}\].
Similarly, 0 is not greater than every rational number.
Thus, option (c) is incorrect.
Let us take the irrational number \[\sqrt 2 \].
Calculating the approximate value of the irrational number \[\sqrt 2 \], we get
\[\sqrt 2 = 1.414\]
Comparing the irrational number \[1.414\] with 0, we get the inequation
\[ \Rightarrow 1.414 > 0\]
We can observe that 0 is lesser than the irrational number \[1.414\], that is \[\sqrt 2 \].
Similarly, 0 is not greater than every irrational number.

Thus, option (d) is incorrect.

Note:
We used the examples of ‘integer’, ‘rational number’, and ‘irrational number’ in the solution.
An integer is a rational number that is not a fraction. For example: 1, \[ - 1\], 3, \[ - 7\], are integers. Integers can be positive like 1, 3, etc. or negative like \[ - 1\].
A rational number is a number which can be written in the form \[\dfrac{p}{q}\], where the denominator \[q \ne 0\]. For example, \[5,\dfrac{7}{2}, - \dfrac{{15}}{7},5.6\], etc. are rational numbers. Rational numbers include every integer, fraction, decimal.
An irrational number is a number which is not a rational number. They cannot be written in the form \[\dfrac{p}{q}\]. For example, \[\sqrt 2 ,\sqrt 5 ,\sqrt 6 \], etc. are irrational numbers.