Tag: real numbers (rational and irrational numbers)

Quizzes (23) Questions (28)

Questions Related to real numbers (rational and irrational numbers)

Multiple choice absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

The value of x on simplifying $x -2 |x|=-3$ is

  1. -1 or 3

  2. 1 or -3

  3. -1 or -3

  4. 1, 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x-2|x| = -3$

There two cases possible either $x$ is positive or$x$ is negative
We have to solve both cases
Firstly taking x as positive
$x-2x=-3$
$x=3$
Now taking $x$ as negative
$x-2(-x)=-3$
$3x=-3$
$x=-1$
So we get two values of $x$ that is -1 and 3
 So correct answer will be option A

Multiple choice absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

If $a$ and $b$ are any real numbers, then which of the following expressions is always positive?

  1. $\left| a \right| $
  2. $\left| a+b \right| $
  3. $\left| a-b \right| +1/2$
  4. ${ a }^{ 2 }+{ b }^{ 2 }$
  5. ${ \left( a+b \right) }^{ 2 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Lets check each option one by one.

A. |a| cab be 0 if a=0 
B. |a+b| can be 0 if a+b=0
C. |a-b|+ 1/2  will always positive because |a+b| is either 0 or positive 
D. ${a}^{2}+{b}^{2}$ can be 0 if both $a$ and $b$ becomes 0
E ${(a+b)}^{2}$ can equal to 0 if $a+b$ = 0
So correct answer will be option C 

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 $0.150150015000...$