Tag: maths

Questions Related to maths

How many hundreds are there in 5127900 ?

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

  1. 9

  2. 900

  3. 90

  4. 9000

Show answer
Correct Option: A

The positive two-digit integers $x$ and $y$ have the same digits, but in reverse order. Which of the following must be a factor of $x + y$? 

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

  1. $6$

  2. $9$

  3. $10$

  4. $11$

  5. $14$

Show answer
Correct Option: D
Explanation:

$\Rightarrow$  Let two positive integers are $x=17$ and $y=71$.

$\Rightarrow$  $x+y=17+71=88$
$\Rightarrow$  $88=11\times 2 \times 2\times 2$
$\therefore$   From the factors given in the options, $11$ will be the factor of $x+y$.

The  expanded form of $67$ is

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

  1. $66+1$

  2. $65+2$

  3. $60 \times 1 + 7$

  4. None of the above

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Correct Option: C
Explanation:

$\Rightarrow$  The given number is $67$.

$\Rightarrow$  The expand form of $67$ = $60\times 1+7$

Expanded form of $78.059$ is:

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

  1. $\displaystyle 78+\frac{5}{10}+\frac{9}{100}$

  2. $\displaystyle 70+8+0+\frac{5}{100}+\frac{9}{1000}$

  3. $\displaystyle 70+8+\frac{5}{10}+\frac{9}{100}$

  4. none

Show answer
Correct Option: B
Explanation:

The expanded form of $78.059$ is

$78+0.059= 70+8+0+\dfrac{5}{100}+\dfrac{9}{1000}$

The general form of $129$ is

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

  1. $100 \times 1 + 10 \times 2 + 9 \times 1$

  2. $120 \times 1 + 9 \times 1$

  3. $100 \times 1 + 30 \times 1 - 1$

  4. All of the above

Show answer
Correct Option: A
Explanation:

General form of a number is denoted by expansion of itself written as sum of multiplication of the digit by its place value.

Therefore, $129$ can be written as $1 \times 100 + 2 \times 10 + 9 \times 1$

The general form of $6.234$ is

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

  1. $6 + \dfrac {200}{10} + \dfrac {3}{100} + \dfrac {4}{1000}$

  2. $6 + \dfrac {2}{10} + \dfrac {30}{100} + \dfrac {4}{1000}$

  3. $60 + \dfrac {2}{10} + \dfrac {3}{100} + \dfrac {4}{1000}$

  4. $6 + \dfrac {2}{10} + \dfrac {3}{100} + \dfrac {4}{1000}$

Show answer
Correct Option: D
Explanation:
Representing the given number in base $10$.
$6.234 = 6\times { 10 }^{ 0 }+2\times { 10 }^{ -1 }+3\times { 10 }^{ -2 }+4\times { 10 }^{ -3 }$
$\Rightarrow 6.234 = 6+ \dfrac { 2 }{ 10 } +\dfrac { 3 }{ 100 } +\dfrac { 4 }{ 1000 } $

The digits in the tens place and units place of a two digit number are $t$ and $u$ respectively. If $1$ is placed between them, what is the value of the three digit number so formed?

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

  1. $100u+t+10$

  2. $100t+10+u$

  3. $10t+u+1$

  4. $100t+10u+1$

Show answer
Correct Option: B
Explanation:

Let the number in one's place be $ u$ and the number in ten's place be $10t$.

According the the question 
$\Rightarrow 10t + 1+ u $
Hence now the 10t will become 100t as it will take hundred's digit place and 1 will become 10 as it will take ten's digit place.
Hence the value  of 3 digit number will be $ 100t + 10 + u $.

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

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

  1. 4

  2. 8

  3. 16

  4. None of these

Show answer
Correct Option: B
Explanation:

$\because $ The number is greater than the number obtained in reversing the digits and the ten's digit is greater than the unit's digit
Let ten's and unit's digit be $2x$ and $x$ respectively
Then, $(10\times 2x+x)-(10x+2x)=36$
$9x=36$
$x=4$
Required difference$=(2x+x)-(2x-x)=2x=8$

$202\times315$ can be expanded as.............

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

  1. $200\times300+300\times15+2\times200+2\times15$

  2. $200\times300+200\times15+2\times300+2\times15$

  3. $200\times3+300\times2+200\times300+2\times15$

  4. $200\times2+300\times15+200\times300+2\times15$

Show answer
Correct Option: B
Explanation:

$202\times 315=63,630$

It can be expanded as,
            $63,630=60,000+3000+600+30$
            $300\times 200+200\times 15+300\times 2+15\times 2$
Therefore, option (B) is correct.

What is the sum of $289$ and $410$ in number name form(i.e. in words)? 

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

  1. Six hundred and ninety two

  2. Six hundred and eighty five

  3. Six hundred and ninety nine

  4. Six hundred and fifty four

Show answer
Correct Option: C
Explanation:
$\Rightarrow$  The given two numbers are $289$ and $410.$
$\therefore$  $289+410=699$
 Hundreds  Tens  Units
$ 6$  $9$ $ 9$

$\therefore$  In word $699$ can be written as "Six hundred and ninety nine."