Tag: expanded form

Questions Related to expanded form

Eighteen lakh nineteen thousand eight hundred eighteen is _________.

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $1,81,81,818$

  2. $18,19,818$

  3. $18,17,818$

  4. None of these

Show answer
Correct Option: B
Explanation:

There are three special numbers in the Indian numbering system – lakh, crore, and arab. A lakh is 1,00,000, 1 , 00 , 000 , a crore is equal to a hundred lakhs and is expressed as 1,00,00,000. An arab is 100 crores and is expressed as 1,00,00,00,000.

So, eighteen lakh nineteen thousand eight hundred eighteen is,
18,19,818
Hence option B is the correct answer

The sum of the reciprocals of $\dfrac {x+3}{x^2+1}$ and $\dfrac {x^2-9}{x^2+3}$ is

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $\dfrac {x^3+2x^2-x}{x^2-9}$

  2. $\dfrac {x^3-2x^2+x}{x^2-9}$

  3. 1

  4. 0

Show answer
Correct Option: B
Explanation:

Consider the sum of the reciprocals of ,

$\dfrac{x+3}{{{x}^{2}}+1}$ and $\dfrac{{{x}^{2}}-9}{{{x}^{2}}+3}$


  $ \Rightarrow \dfrac{{{x}^{2}}+1}{x+3}+\dfrac{{{x}^{2}}+3}{{{x}^{2}}-9}=\dfrac{{{x}^{2}}+1}{x+3}+\dfrac{{{x}^{2}}+3}{\left( x-3 \right)\left( x+3 \right)} $

 $ \Rightarrow \dfrac{\left( {{x}^{2}}+1 \right)\left( x-3 \right)+{{x}^{2}}+3}{\left( x-3 \right)\left( x+3 \right)} $

 $ \Rightarrow \dfrac{{{x}^{3}}-3{{x}^{2}}+x-3+{{x}^{2}}+3}{\left( x-3 \right)\left( x+3 \right)} $

 $ \Rightarrow \dfrac{{{x}^{3}}-2{{x}^{2}}+x}{\left( x-3 \right)\left( x+3 \right)} $

 $ \Rightarrow \dfrac{{{x}^{3}}-2{{x}^{2}}+x}{\left( x^2-9 \right)} $

Number of zeroes in $100$ million are ___________.

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $8$

  2. $7$

  3. $9$

  4. $6$

Show answer
Correct Option: A
Explanation:
1 million = 1,000,000
100 million = 100,000,000
Number of zeroes = 8

Expanded form of $27012$ is

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $2000 + 700 + 0 + 10 + 2$

  2. $20000 + 700 + 0 + 10 + 2$

  3. $20000 + 1000 + 0 + 70 + 2$

  4. $20000 + 7000 + 0 + 10 + 2$

Show answer
Correct Option: D
Explanation:

Expanded form of 27012 is

=20000+7000+000+10+2

Expanded form of $920,831$

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $90000 + 20000 + 800 + 1$

  2. $9200 + 800 + 31$

  3. $90000 + 20000 + 800 + 30 + 1$

  4. $900000 + 20000 + 800 + 30 + 1$

Show answer
Correct Option: D
Explanation:

Expanded form of 920,831

= 900000+20000+800+30+1

If $n$ is an integer, which of the following must be an even integer?

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $n+1$

  2. $n+2$

  3. $2n$

  4. $2n+1$

  5. $\displaystyle { n }^{ 2 }$

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  The number which is multiple of $2$ is called an even number.

$\Rightarrow$  It is given that $n$ is an integer.
$\Rightarrow$  So, $2n$ will be an even number.

The  expanded form of $999$ is

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $1000 - 3$

  2. $1005 - 6$

  3. $1000 \times 1 -1$

  4. None of the above

Show answer
Correct Option: D
Explanation:

$999 = 100 \times 9 + 9\times10+9$

The expanded form of $99$ is

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $97+2$

  2. $100-1$

  3. $10 \times 9+9$

  4. None of the above

Show answer
Correct Option: C
Explanation:

$99 = 10 \times 9 + 9$

The expanded form of $72$ is

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $10 \times 7+2$

  2. $71+1$

  3. $73-1$

  4. None of the above

Show answer
Correct Option: A
Explanation:

$72 = 10 \times 7 + 2$

The general form of $11$ is

maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

  1. $10 \times 0+11$

  2. $10 \times 2+1$

  3. $10 \times 1 + 1$

  4. None of the above

Show answer
Correct Option: C
Explanation:

$11 = 10 \times 1 + 1$


So, option C is correct