Mathematics · Quantitative Aptitude

Real Number System

261 Questions

The real number system encompasses rational and irrational numbers, forming the basis of arithmetic and number theory. It is a key area in the quantitative aptitude and mathematics sections of school level and competitive exams. Practice these questions to master the properties and identification of different types of numbers.

Identifying irrational numbersOrdering rational numbersProperties of square rootsPerfect number propertiesRational and irrational products

Real Number System Questions

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Which of the following rational number lies between $\dfrac {4}{9}$ and $\dfrac {4}{5}$?

  1. $-1$
  2. $\dfrac {28}{45}$
  3. $0$
  4. $1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$Mean = \dfrac{\left (\dfrac {4}{9} + \dfrac {4}{5}\right )}{2} = \left (\dfrac {20 + 36}{45}\right ) \times \dfrac {1}{2} = \dfrac {56}{45}\times \dfrac {1}{2}$
$= \dfrac {28}{45}$

Mean of two numbers always lies between the two numbers.
So, answer is option $B.$ 

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Choose the rational number, which does not lie, between the rational numbers, $\dfrac{-2}{3}$ and $\dfrac{-1}{5}$

  1. $\dfrac{-3}{10}$
  2. $\dfrac{3}{10}$
  3. $\dfrac{-1}{4}$
  4. $\dfrac{-7}{20}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given rational numbers $-\dfrac { 2 }{ 3 }$ and $-\dfrac { 1 }{ 5 }$ are negative rational numbers because the numerator and denominator of both the rational numbers are of opposite signs that is the numerator of both the integers is negative while the denominators are positive.


Therefore, none of the positive rational number can lie between the given negative rational numbers $-\dfrac { 2 }{ 3 }$ and $-\dfrac { 1 }{ 5 }$.


Hence, $\dfrac { 3 }{ 10 }$ does not lie between the rational numbers $-\dfrac { 2 }{ 3 }$ and $-\dfrac { 1 }{ 5 }$.

Multiple choice maths operations on rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Rational number between $\dfrac{3}{8}$ and $\dfrac{7}{12}$ are 

  1. $\dfrac{3}{8},\dfrac{41}{96},\dfrac{23}{48},\dfrac{7}{12}$
  2. $\dfrac{3}{8},\dfrac{41}{196},\dfrac{23}{48},\dfrac{7}{12}$
  3. $\dfrac{3}{8},\dfrac{41}{96},\dfrac{23}{148},\dfrac{7}{12}$

  4. None of the above.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

3/8 = 0.375 and 7/12 = 0.5833. Option A: 41/96 = 0.427 and 23/48 = 0.479. Both are between 0.375 and 0.5833.

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The rational form of $-25.6875$ is

  1. $\displaystyle-\frac{411}{16}$
  2. $\displaystyle-\frac{421}{16}$
  3. $\displaystyle-\frac{431}{16}$
  4. $\displaystyle-\frac{441}{16}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Consider the given decimal number

$ \Rightarrow -25.6875 $

$ \Rightarrow -\dfrac{256875}{10000} $

$ \Rightarrow -\dfrac{51375}{2000} $

$ \Rightarrow -\dfrac{10275}{400} $

$ \Rightarrow -\dfrac{2055}{80} $

$ \Rightarrow -\dfrac{411}{16} $


Hence, this is the answer.

Multiple choice

What is the name of the mathematical constant approximately equal to 2.71828?

  1. Euler's Number

  2. Golden Ratio

  3. Pi

  4. Avogadro's Number
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Euler's Number, also known as the base of the natural logarithm, is approximately equal to 2.71828.