Tag: number system

Quizzes (32) Questions (18)

Questions Related to number system

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

Which of the following numbers lie between $1$ and $3$?

  1. $\dfrac13$
  2. $\sqrt{2}$
  3. $\sqrt{10}$
  4. $\dfrac{8}3$
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

Converting all option in decimal format (approximately)

A. $\frac{1}{3}=0.33$
B.$\sqrt {2  } =1.41$
C.$ \sqrt { 10 }=3.16 $
D. $\frac{8}{3}=2.67$
It is clear that option B and D lies between 1 and 3
So correct answer will be option B and D

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

Between any $2$ real numbers, __________ can always be represented on a number line.

  1. an integer

  2. an irrational number

  3. a natural number

  4. a rational number
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

Between any two real number, there is always many rational number.

And between any two rationals there is always an irrational numbers.
Thus, we can represent rationals and irrationals between any two reals.
Hence, option B and D is correct.

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

Following are the steps to represent $\sqrt5$  on number line.
Arrange them in order.
1) Draw OC on line with $l(OC)=l(OB)$,
2) Draw $AB \perp OA\ and\ l(AB) =1$
3) Take $l(OA)=2$
4) $l(OC)=\sqrt5$, C is required point on real line.

  1. $1,2,3,4$
  2. $2,4,1,3$
  3. $3,2,4,1$
  4. $3,2,1,4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The correct order of representing $\sqrt { 5 } $ on number line is 

Step 1. Take $l(OA) = 2$.
Step 2. Draw $AB$$\perp $$OA\ and\  l(AB)$ $= 1$
Step 3. Draw $OC$ on line with $l(OC) = l(OB)$
Step 4. $l(OC) =$ $\sqrt { 5 } $, $C$ is the required point on real line
Therefore, option(D) is correct.

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

Which of the following irrational numbers lie between $6$ and $8$?

  1. $\sqrt{49}$
  2. $\sqrt{19}$
  3. $\sqrt{47}$
  4. $\sqrt{62}$
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

$6^{2} = 36$

$7^{2} = 49$
$8^{2} = 64$

$\Rightarrow \sqrt47$ and $\sqrt62$ are only irrational numbers from the stated that lie in between $6$ and $8$.

$\sqrt49 = 7$ which isn't irrational.

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

The greater number between $\sqrt{17}-\sqrt{12}$ and $\sqrt{11}-\sqrt{6}$ is ____.

  1. $\sqrt{17}-\sqrt{12}$
  2. $\sqrt{11}-\sqrt{6}$

  3. Both are equal

  4. Cannot comare
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\sqrt{17}=4.12\ \sqrt {12}=3.46\ \therefore\sqrt{17}-\sqrt{12}=0.66$

$\sqrt{11}=3.32\ \sqrt6=2.45\ \therefore\sqrt{11}-\sqrt6=0.87$

$\sqrt{11}-\sqrt6>\sqrt{17}-\sqrt{12}$

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

The value of $0.\overline{2}$ in the form $\frac{p}{q}$ , where p and q are integers and $q\ne 0$ is :

  1. $\dfrac{1}{5}$
  2. $\dfrac{2}{9}$
  3. $\dfrac{2}{5}$
  4. $\dfrac{1}{8}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$Let\quad x=.222....\ On\quad multiplying\quad by\quad 10\quad on\quad both\quad sides\quad \ 10x=2.222....\ On\quad subtracting\quad both\quad equations\quad \ 9x=2\ x=\dfrac { 2 }{ 9 } $

Hence,correct answer is option B.

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

Which of the following is/are correct?

  1. Every integer is a rational number.

  2. The sum of a rational number and an irrational number is an irrational number.

  3. Every real number is rational.

  4. Every point on the number line is associated with a real number
Reveal answer Fill a bubble to check yourself
A,B,D Correct answer
Explanation

Yes every integer can be represented in the form of $p/q$ where q is 1 for integers, so every integer is a rational number.
The sum of rational and irrational numbers is always irrational.
No, every real number is not rational. Real numbers are classified as rational numbers and irrational numbers.
Any number on the number line is a real number because that number can be either rational or irrational. Rational and irrational numbers together form real numbers.

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

To represent a rational number $\sqrt{2}$ on number line, take sides of right triangle as:

  1. $1$ and $1$
  2. $1$ and $2$
  3. $2$ and $0$
  4. $-1$ and $-1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Notice that $\sqrt{2}= \sqrt{(1^2 + 1^2)}$. So, we can form a length of $\sqrt{2}$ units using two mutually perpendicular sides of length $1$ unit each. (Since, $1,1,\sqrt{2}$ form sides of a right angled triangle by Pythagoras theorem).