Tag: rational numbers between two rational numbers

Questions Related to rational numbers between two rational numbers

Write three rational numbers between $\displaystyle \sqrt{3}$ and $\displaystyle \sqrt{5}$.

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

  1. 1.8,2 and 2.2

  2. 1.6,2 and 2.2

  3. 1.8,2.2 and 2.4

  4. none of the above

Show answer
Correct Option: A
Explanation:

We know that, $ \sqrt {3} = 1.732$ and $ \sqrt {5} = 2.236 $

Hence three rational numbers between $ 1.732 $ and $ 2.236$  can be $ 1.8 \left(= \dfrac {18}{10}\right)  $ , $ 2 $ and $ 2.2 \left(= \dfrac {22}{10}\right) $.

Which one of the following is the rational number lying between $\displaystyle \frac{6}{7} \ and \ \frac{7}{8}?$

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

  1. $\displaystyle \frac{3}{4}$

  2. $\displaystyle \frac{99}{122}$

  3. $\displaystyle \frac{95}{112}$

  4. $\displaystyle \frac{97}{112}$

Show answer
Correct Option: D
Explanation:

Required rational number $\displaystyle =\frac{1}{2}\left ( \frac{6}{7}+\frac{7}{8} \right )=\frac{1}{2}\left ( \frac{48+49}{56} \right )=\frac{97}{112}$
Hence option (d) is correct

The number of integers between $\displaystyle -\sqrt{8}: and: \sqrt{32} $ is

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

  1. 5

  2. 6

  3. 7

  4. 8

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Correct Option: D
Explanation:
We will find the number of integers as follows,
√8 = 2.8 ( approximately )
- √8 = - 2.8
√32 = 5.6 ( approximately )
Now integers between -2.8 and 5.6 are
-2, -1, 0, 1, 2, 3, 4, 5
and a total of 8 numbers
Option D is the correct answer.

Identify a rational number between $\sqrt{2}$ and $\sqrt{3}$.

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

  1. $\dfrac{\sqrt{2}.\sqrt{3}}{2}$

  2. $1.5$

  3. $1.8$

  4. $\dfrac{\sqrt{2}+\sqrt{3}}{2}$

Show answer
Correct Option: B
Explanation:

As $\sqrt 6$ is irrational therefore option A is wrong.

$1.5$ is rational and it lies between $\sqrt 2$ & $\sqrt 3$ hence Option B is correct.
$1.8$ is rational but it doesn't lies between $\sqrt {2}$ & $\sqrt 3$ implies option C is wrong.
As sum of $\sqrt 2$ & $\sqrt 3$ is irrational therefore option D is also wrong.

Which are three rational numbers between $-2$ and $-1$?

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

  1. $\dfrac { -1 }{ 2 } ,\dfrac { -1 }{ 3 } ,\dfrac { -1 }{ 5 } $

  2. $\dfrac { -3 }{ 2 } ,\dfrac { -7 }{ 4 } ,\dfrac { -5 }{ 4 } $

  3. $\dfrac { -12 }{ 5 } ,\dfrac { -22 }{ 5 } ,\dfrac { 12 }{ 5 } $

  4. $\dfrac { 3 }{ 2 } ,\dfrac { 7 }{ 4 } ,\dfrac { 5 }{ 4 } $

Show answer
Correct Option: B
Explanation:

In option B,


$\dfrac{-3}{2} = -1.5$

$\dfrac{-7}{4} = -1.75$

$\dfrac{-5}{4} = -1.25$

All these numbers lie in between $(-2,-1)$

The rational number between the pair of number $\dfrac{1}{2}$ and $\sqrt 1$ is:

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

  1. $\dfrac{9}{4}$

  2. $\dfrac{3}{4}$

  3. $\dfrac{5}{4}$

  4. $\dfrac{7}{4}$

Show answer
Correct Option: B
Explanation:

The rational number between $\dfrac12$ and $\sqrt1$ :

Since, $\sqrt1=1$
So. the rational number between $\dfrac12$ and $1=\dfrac12\times \left(\dfrac12+1\right)$
$=\dfrac12 \times \dfrac32$
$=\cfrac34$
So, $B$ is the correct option.

The rational number which is not lying between $\displaystyle\frac{5}{16}$ and $\displaystyle\frac{1}{2}$ is _________.

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

  1. $\displaystyle\frac{3}{8}$

  2. $\displaystyle\frac{7}{16}$

  3. $\displaystyle\frac{1}{4}$

  4. $\displaystyle\frac{13}{32}$

Show answer
Correct Option: C
Explanation:

We know $\dfrac{5}{16} =0.3125$

and $\dfrac{1}{2}= 0.5$
Option A: $\dfrac{3}{8} =0.375$
lying between the gven numbers

Option B: $\dfrac{7}{16}= 0.4375$
lying between the given numbers.

Option C: $\dfrac{1}{4}=0.25$
NOT lying between the given numbers.

Option D: $\dfrac{13}{32}=0.40625$
lying between the given numbers.
So, option C is correct.

A rational number lie between $\displaystyle\frac{1}{4}$ and $\displaystyle\frac{1}{3}$ is _________.

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

  1. $\displaystyle\frac{7}{24}$

  2. $0.29$

  3. $\displaystyle\frac{13}{48}$

  4. All of these

Show answer
Correct Option: D
Explanation:

We know $\dfrac{1}{4} = 0.25$

and $\dfrac{1}{3}=0.3333333$

Option A: $\dfrac{7}{24}$
$=0.291666$
lies between the given numbers

Option B: $ 0.29$
lies between the given numbers

Option C: $\dfrac{13}{48}$
$=0.27083333$
lies between the given numbers.

All the options are correct.

Number of rational numbers between $15$ and $18$ is:

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

  1. infinite

  2. finite

  3. zero

  4. one

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Correct Option: A
Explanation:

Between any two rational numbers we can find infinitely many rational numbers. 

Thus, number of rational numbers between $15$ and $18$ is infinite.
Hence, the answer is infinite.

A rational number -2/3 ______ .

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

  1. Lies to the left side of 0 on the number line.

  2. Lies to the right side of 0 on the number line.

  3. It is not possible to represent on the number line.

  4. Cannot be determined on which side the number lies.

Show answer
Correct Option: A
Explanation:

rational number always lies on the line.

 this rational number is $\dfrac{-2}{3}$ which is negative  hence it is always lies to left side of $0$ on the number line.
hence option $A$ is correct.