Tag: representation of rational numbers on number line

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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

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

  1. $\dfrac {3}{8}$
  2. $\dfrac {7}{16}$
  3. $\dfrac {1}{4}$
  4. $\dfrac {13}{32}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

5/16 = 0.3125 and 1/2 = 0.5. Comparing options: 3/8 = 0.375 (in range), 7/16 = 0.4375 (in range), 1/4 = 0.25 (not in range), 13/32 = 0.40625 (in range).

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

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

  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. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 0.9 < 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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


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

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

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

  1. $1.5,\ 1.6$
  2. $1.4,\ 1.6$
  3. $1.5,\ 1.8$

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
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}) $

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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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) $.

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

  1. $\displaystyle \frac{3}{4}$
  2. $\displaystyle \frac{99}{122}$
  3. $\displaystyle \frac{95}{112}$
  4. $\displaystyle \frac{97}{112}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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

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

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

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
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.
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

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

  1. $\dfrac{\sqrt{2}.\sqrt{3}}{2}$
  2. $1.5$
  3. $1.8$
  4. $\dfrac{\sqrt{2}+\sqrt{3}}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

  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 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $(-2,-1)$

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

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

  1. $\dfrac{9}{4}$
  2. $\dfrac{3}{4}$
  3. $\dfrac{5}{4}$
  4. $\dfrac{7}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $\displaystyle\frac{3}{8}$
  2. $\displaystyle\frac{7}{16}$
  3. $\displaystyle\frac{1}{4}$
  4. $\displaystyle\frac{13}{32}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.