Tag: fractions, decimals and rational numbers

Questions Related to fractions, decimals and rational numbers

The rational number is not lying between $\dfrac {5}{16}$ and $\dfrac {1}{2}$ 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. $\dfrac {3}{8}$

  2. $\dfrac {7}{16}$

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

  4. $\dfrac {13}{32}$

Show answer
Correct Option: C

Find 9 rational numbers between  $2$ and $3$

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. $2 < 2.1 < 2.2 < 3.3 < 2.4 < ... < 2.9 < 3$

  2. $2 < 4.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$

  3. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$

  4. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 0.9 < 3$

Show answer
Correct Option: C
Explanation:

$2 < 2.1=(2+0.1) < 2.2=(2.1+0.1) < 2.3=(2.2+0.1) < 2.4=(2.3+0.1) < ... < 2.9=(2.8+0.1) < 3=(2.9+0.1)$


$2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$

Write two rational numbers between $\displaystyle \sqrt{2}$ and $\displaystyle \sqrt{3}.$

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. $1.5,\ 1.6$

  2. $1.4,\ 1.6$

  3. $1.5,\ 1.8$

  4. none of the above

Show answer
Correct Option: A
Explanation:

We know that, $ \sqrt {2} = 1.414

$ and $ \sqrt {3} = 1.732 $

Hence two rational numbers between $ 1.414 $ and $ 1.732

$  can be $ 1.5 (= \frac {3}{2}) $ and $ 1.6 (= \frac {16}{10}= \frac {8}{5}) $

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

Show answer
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.