Tag: rational and irrational numbers

Quizzes (6) Questions (185)

Questions Related to rational and irrational numbers

Multiple choice decimal representation of rational numbers rational and irrational numbers maths

If a and b are any two such real numbers that ab $ = 0 $ , then

  1. $a = 0, b \leq 0$
  2. $b = 0, a \leq 0$

  3. a = 0 or b = 0 or both
  4. $a = b$ and $b = 0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

if both number are real the either a or b or both should be zero.
then only ab will be 0.
if any real number is multiplied by 0 then result will be zero.
So, answer is
C a = 0 or b = 0 or both

Multiple choice decimal representation of rational numbers rational and irrational numbers maths

If $f(x)-2f(1-x) = x^2+2$, then what is $f(x)$?

  1. $f(x)=-x^2+\dfrac{4}{3}x-\dfrac{3}{8}$
  2. $f(x)=−x^2+\dfrac{4}{3}x−\dfrac{8}{3}$
  3. $f(x)=−x^2+\dfrac{8}{3}x−\dfrac{4}{3}$
  4. $f(x)=−x^2+\dfrac{3}{8}x−\dfrac{3}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$f\left(x\right)-2f\left(1-x\right)={x}^{2}+2$      .......$(1)$

Setting $x=1-x$ then we get

$f\left(1-x\right)-2f\left(1-1+x\right)={\left(1-x\right)}^{2}+2$ 

$f\left(1-x\right)-2f\left(x\right)={x}^{2}-2x+3$ 

$2f\left(1-x\right)-4f\left(x\right)=2{x}^{2}-4x+6$    .......$(2)$

Adding $(1)$ and $(2)$ we get

$-3f\left(x\right)=3{x}^{2}-4x+8$ 

$\therefore f\left(x\right)=-{x}^{2}+\dfrac{4}{3}x-\dfrac{8}{3}$ 
Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State whether the following statement is True or False:
A rational and Irrational number between $2.357$ and $3.121$ is $3, 3.101101110 ...$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Any terminating decimal between 2.357 and 3.121 will be a rational number like, ${3}$

Any non-terminating and non-recurring decimal between  2.357 and 3.121 will be an irrational number like $3.101101110...$

Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State the following statement is True or False
A rational number between  $3.623623$ and  $0.484848 $ are $4$ and $4.909009000 .$..

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$4>3.623623$ and $4.90900900...>3.623623$

Since both the numbers do not lie between $0.4848$ and $3.623623.$, the given statement is false. 

Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State true or false:
The three rational numbers between $\displaystyle \sqrt{3}$ and $\displaystyle \sqrt{5}$ are 1.6, 1.8, 2.2

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B 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( = \frac {18}{10}) ; 2 $ and $ 2.2 (= \frac {22}{10}) $


Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State the following statement is true or false:
$\dfrac{5}{12}$  lies between $\cfrac{1}{3}$ and $\cfrac{1}{2}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average of the two numbers will be in between the two numbers.
$ \cfrac { \left( \dfrac { 1 }{ 3 }  \right) +\left( \dfrac { 1 }{ 2 }  \right)  }{ 2 } $

$= \cfrac { \left( \dfrac { 5 }{ 6 }  \right)  }{ 2 } $

$= \dfrac { 5 }{ 12 } $ is a rational number which lies between $\dfrac{1}{3}\ and\ \dfrac{1}{2}$. 




Multiple choice irrational numbers irrational numbers and their operations rational and irrational numbers real numbers (rational and irrational numbers) maths

State whether the given statement is true/false.
An irrational number between two numbers $\dfrac{1}{7}$ and $\dfrac{2}{7}$ is $0.1501500 15000...$ .

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let us first find the decimal forms of the given numbers as follows: 
 
$\dfrac { 1 }{ 7 } =0.\overline { 142857 } ,\dfrac { 2 }{ 7 } =0.\overline { 285714 }$

We find a number which is non-terminating non-recurring lying between them.
So, we can find infinite many such numbers. For example, $0.150150015000...$ and $0.20200200020000....$

Hence, an irrational number between two numbers $\dfrac {1}{7}$ and $\dfrac {2}{7}$ is $0.150150015000...$
Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

If $\sqrt{a}$ is an irrational number, what is a? 

  1. Rational

  2. Irrational
  3. $0$

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

Consider the given irrational number$\sqrt{a}$ ,

Definition  of rational number- which number can be write in the form of $\dfrac{p}{q}$ but $q\ne 0$ is called rational number.

Hence, $a=\dfrac{a}{1}$

That why  $a$ is rational number

 

Hence, this is the answer.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which of the following is irrational

  1. $\sqrt {\dfrac{4}{9}} $
  2. $\dfrac{4}{5}$
  3. $\sqrt 7 $
  4. $\sqrt {81} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
A $=\sqrt{\dfrac{4}{9}}=\dfrac{2}{3}$         Rational

B $=\dfrac{4}{5}$                       Rational

C $=\sqrt7$                     Irrational

D $=\sqrt{81}=9$          Rational