Tag: representation of rational numbers on number line

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Questions Related to representation of rational numbers on number line

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

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

  1. $\displaystyle\frac{7}{24}$
  2. $0.29$
  3. $\displaystyle\frac{13}{48}$

  4. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. infinite

  2. finite

  3. zero

  4. one
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

A rational number -2/3 ______ .

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

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
Among the following 
$-\frac{3}{2},-1,3,0,\frac{1}{2}$
find the rational numbers less than $2.$
  1. $0$
  2. $-\frac{3}{2}$
  3. $-1$
  4. $\frac{1}{2}$
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

$\dfrac{-3}{2},-1,3,0,\dfrac{1}{2}$


$-1.5,-1,3,0,0.5$


$\implies $ Among five rational numbers $-1.5,-1,0,0.5$ are lesser than $2$ expect $3$.


All options are 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

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

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

For a rational number to lie between $\dfrac{-2}{5}$ and $\dfrac{-1}{5}$,it should be less than $\dfrac{-1}{5}$ and greater than $\dfrac{-2}{5}$.
Now,$\dfrac{3}{10}$ is not less than $\dfrac{-1}{5}$.
So,$\dfrac{3}{10}$ does not lie between $\dfrac{-1}{5}$ and $\dfrac{-2}{5}$.

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

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

  1. $\dfrac{46}{75}$
  2. $\dfrac{47}{75}$
  3. $\dfrac{49}{75}$
  4. $\dfrac{50}{75}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

All the options have denominator $75$. Hence, let us convert into equivalent fractions having denominator $75$. 
$\dfrac{3}{5} $ $=\dfrac{3\times 15}{5\times 15} $ $=\dfrac{45}{75}$

$\dfrac{2}{3}$ $=\dfrac{2\times 25}{3\times 25}$ $=\dfrac{50}{75}$

Hence, $\dfrac{50}{75}$ does not lie between the given numbers.

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

Rationalising the denominator of $\dfrac {5}{\sqrt 3-\sqrt 5}$ is -

  1. $(\frac {5}{2}(\sqrt 3+\sqrt 5)$
  2. $(-\frac {5}{2}(\sqrt 3+\sqrt 5)$
  3. $(\frac {5}{2}(\sqrt 3-\sqrt 5)$
  4. $(-\frac {5}{2}(\sqrt 3-\sqrt 5)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

here, $\dfrac {5}{\sqrt 3-\sqrt 5}$

$=\dfrac {5}{\sqrt 3-\sqrt 5}\times \dfrac {\sqrt 3+\sqrt 5}{\sqrt 3+\sqrt 5}$

$=\dfrac {5(\sqrt 3+\sqrt 5)}{3-5}$


$=-\dfrac {5}{2}(\sqrt 3+\sqrt 5)$

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

A train of length 180 m crosses a man standing on a platform in 12 seconds and cross another train coming from opposite direction in 12 sec. If the second train running at 2/3 rd speed of the firstthen find the length of the second train?

  1. 56

  2. 120

  3. 20

  4. 44
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Length of the first train$=180m$


 Time taken by  the train to cross the man standing on the platform$=12s$


Speed of the first train$=\dfrac{180}{12}$

                                      $=15m/s$

Speed of the second train$=\dfrac{2}{3}\times15$

                                            $=10m/s$

Relative speed$=15+10$

                          $=25m/s$
 
Let the length of the train be $y$ metres.

$Distance =Speed\times time$

$y+180=25\times12$

$y+180=300$

$y=300-180$
$y=120$
So, the length of the second train$=120m$