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Concepts of seven and eight digit numbers - class-VI

Description: concepts of seven and eight digit numbers
Number of Questions: 36
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Tags: large numbers number work whole numbers and operations with whole numbers concepts of seven and eight digit numbers place value numbers operations on rational numbers maths numbers in indian and international systems knowing our numbers know the numbers numbers and place value
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The number of zeroes that comes after $1$ for $10$ millions are

maths number work indian place value chart place value of digit largest and smallest numbers writing and expanding numbers

  1. $8$

  2. $7$

  3. $6$

  4. $9$

Show answer
Correct Option: B
Explanation:

Million $=1,000,000$ ($6$ zeros)
$10$   million $=10,000,000$
Hence the number of zeros after $1$ in $10$ million is $7.$

Match the following.

Column I Column II 
(i). 100 crores (P) 1 thousand
(ii) 10 lakhs (Q) 1 lakh
(iii) 100 thousands (R) 1 billion
(iv) 100 tens (S) 1 million
maths number work indian place value chart place value of digit largest and smallest numbers writing and expanding numbers

  1. (i)>(P), (ii) > (Q), (iii) > (S), (iv) > (R)

  2. (i)>(R), (ii) > (S), (iii) > (P), (iv) > (Q)

  3. (i)>(R), (ii) > (S), (iii) > (Q), (iv) > (P)

  4. (i)>(P), (ii) > (S), (iii) > (Q), (iv) > (R)

Show answer
Correct Option: C
Explanation:

(i) $100$ crores $= 1,000,000,000 = 1$ billion (R)

(ii) $10$ lakhs $= 1,000,000 =  1$ million (S)
(iii) $100$ thousands $= 1,00,000 = 1$ lakh (Q)
(iv) $100$ tens $= 1,000 = 1$ thousand (P)

A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

maths number work indian place value chart place value of digit largest and smallest numbers writing and expanding numbers

  1. 20 m

  2. 30 m

  3. 40 m

  4. 50 m

Show answer
Correct Option: D
Explanation:
Let the length of the train be x metres and speed  be y $m/s$

Speed of the first person$=2kmph$

                                          $=2\times\dfrac{5}{18}$

                                            $=\dfrac{5}{9}m/s$

Speed of the second train $=4kmph$

                                              $=4\times\dfrac{5}{18}$

                                               $=\dfrac{10}{9}m/s$

$\dfrac{x}{y-\dfrac{5}{9}}=9$

$9y-5=x$   
                                       
$90y-50=10x$...........................................(1)

                                            
$\dfrac{x}{y-\dfrac{10}{9}}=10$

$90y-100=9x$...........................................(2)

Substracting $1$ and $2$

$90y-50-90y+100=10x-9x$

$x=50$

So, the length of the train$=50m$



Express in Indian system of numeration.
Three million four hundred thirty five thousand two hundred twenty five.

maths number work indian place value chart place value of digit largest and smallest numbers writing and expanding numbers

  1. $345,225$

  2. $34,352,25$

  3. $3,43,52,25$

  4. $34,35,225$

Show answer
Correct Option: D
Explanation:

Let us convert the given number in words into numerals as follows:


Three million$=30,00,000$
Four hundred thirty five thousand$=435,000$
Two hunderd$=200$
Twenty$=20$
Five$=5$

Now, add the numerals as shown below:

$3000000+435000+200+20+5=34,35,225$

Therefore, the required number is $34,35,225$.

Hence, the Indian system of numeration is $34,35,225$.

Express in Indian number system:
$35,987,123$

maths number work indian place value chart place value of digit largest and smallest numbers writing and expanding numbers

  1. $35,987,123$

  2. $3,59,87,123$

  3. $3,987,123$

  4. $3,59,8,71,23$

Show answer
Correct Option: B
Explanation:
Let us convert the given numerals into words as follows:

$3,00,00,000=$Three crores
$59,00,000=$Fifty nine lakh
$87,000=$Eighty seven thousand
$100=$One hundred
$20=$Twenty
$3=$Three

Therefore, the number can be written in words as Three crores fifty nine lakh eighty seven thousand one hundred and twenty three.

Now, add the above numerals as shown below:

$3,00,00,000+59,00,000+87,000+100+20+3=3,59,87,123$ 
where $3$ is at one's place, $2$ is at tens place, $1$ is at hundredth place, $7$ is at thousandth place and so on. 

Hence, the Indian number system is $3,59,87,123$.

Express in Indian number system.
$4,456,765$

maths number work indian place value chart place value of digit largest and smallest numbers writing and expanding numbers

  1. Four crore forty five lakh seven hundred sixty five,

  2. Forty four lakh fifty six thousand seven hundred sixty five,

  3. Forty four crore forty five lakh seven hundred sixty five,

  4. Forty five lakh seven hundred sixty five,

Show answer
Correct Option: B
Explanation:
Let us convert the given numerals into words as follows:

$44,00,000=$Forty four lakh
$56,000=$Fifty six thousand
$700=$Seven hundred
$60=$Sixty
$5=$Five

Now, combine the numbers in words as shown below:

Fourty four lakh fifty six thousand seven hundred sixty five.

Hence, the Indian number system is fourty four lakh fifty six thousand seven hundred sixty five.

A data has highest value $120$ and the lowest value $71.A$ frequency distribution in descending order with seven classes is to be constructed. The limits of the second class interval shall be 

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $77$ and $78$

  2. $78$ and $85$

  3. $85$ and $113$

  4. $113$ and $120$

Show answer
Correct Option: D
Explanation:
Range of Frequency distribution=Highest Value-Lowest value
 $=120-71=49$

Dividing this into Seven $(7)$ equal classes.

$\Rightarrow \dfrac{49}{7}=7$

Thus the class width should be 7

Now  arranging  in descending order

Class interval $1 \rightarrow (120-7) to\space 120 \rightarrow 113-120$

Class interval $2 \rightarrow (113-7) to \space 113 \rightarrow 106-113$

Hence class interval $1$ and $2$ is $113$ and $120$ 

Arrange the following fractions is ascending order :
$\dfrac{7}{10},\dfrac{3}{8},\dfrac{4}{5}$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac{3}{8},\dfrac{7}{10},\dfrac{4}{5}$

  2. $\dfrac{3}{8},\dfrac{4}{5},\dfrac{7}{10}$

  3. $\dfrac{4}{5},\dfrac{3}{8},\dfrac{7}{10}$

  4. $\dfrac{7}{10},\dfrac{3}{8},\dfrac{4}{5}$

Show answer
Correct Option: A
Explanation:
$7/10= 0.7$
$3/8 = 0.375$
$4/5=0.8$

So ascending order, = $\dfrac 3 8, \dfrac 7 {10}, \dfrac 4 5$

Arrange the following rational number in ascending order $\displaystyle \frac{3}{7},\frac{4}{5},\frac{7}{9},\frac{1}{2}$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\displaystyle \frac{4}{5},\frac{7}{5},\frac{3}{9},\frac{1}{2}$

  2. $\displaystyle \frac{3}{7},\frac{1}{2},\frac{7}{9},\frac{4}{5}$

  3. $\displaystyle \frac{4}{5},\frac{7}{9},\frac{1}{2},\frac{3}{7}$

  4. $\displaystyle \frac{1}{2},\frac{3}{7},\frac{7}{9},\frac{4}{5}$

Show answer
Correct Option: B
Explanation:

The LCM of 2, 5, 7 and 9 is 630.
$\frac{3}{7} = \frac{270}{630}$
$\frac{4}{5} = \frac{504}{630}$
$\frac{7}{9}=\frac{490}{630}$
$\frac{1}{2}=\frac{315}{630}$
The ascending order will be $\frac{3}{7},\frac{1}{2},\frac{7}{9},\frac{4}{5}$

Arrange in ascending order of magnitude $\sqrt 3, \sqrt [5]{15}, \sqrt [10]{227}$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\sqrt [5]{15} < \sqrt [10]{227} < \sqrt 3$

  2. $\sqrt 3 < \sqrt [5]{15} < \sqrt [10]{227}$

  3. $\sqrt [10]{227} < \sqrt 3 < \sqrt [5]{15}$

  4. None of these

Show answer
Correct Option: A
Explanation:

$\sqrt 3, \sqrt [5]{15}, \sqrt [10]{227}$


LCM of $2, 5$ and $10=10$

$\sqrt 3=\sqrt [2\times 5]{3^5}=\sqrt [10]{3\times 3\times 3\times 3\times 3}=\sqrt [10]{243}$

$\sqrt [5]{15}=\sqrt [5\times 2]{15^2}=\sqrt [10]{15\times 15}=\sqrt [10]{225}$

$\sqrt [10]{227}=\sqrt [10]{227}$

$\therefore \sqrt [5]{15} < \sqrt [10]{227} < \sqrt 3$

Arrange the given fractions in ascending order:

$\displaystyle\frac{2}{7}$, $\displaystyle\frac{4}{5}$, $\displaystyle\frac{3}{4}$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\displaystyle\frac{4}{5}$, $\displaystyle\frac{3}{4}$, $\displaystyle\frac{2}{7}$

  2. $\displaystyle\frac{4}{5}$, $\displaystyle\frac{2}{7}$, $\displaystyle\frac{3}{4}$

  3. $\displaystyle\frac{2}{7}$, $\displaystyle\frac{3}{4}$, $\displaystyle\frac{4}{5}$

  4. $\displaystyle\frac{3}{4}$, $\displaystyle\frac{2}{7}$, $\displaystyle\frac{4}{5}$

Show answer
Correct Option: C
Explanation:

First, we make all divisors common.
So l.c.m of $7,5,4 = 140$


Now $\dfrac{2}{7}\times \dfrac{20}{20} = \dfrac{40}{140}$

$\dfrac{4}{5}\times \dfrac{28}{28} = \dfrac{112}{140}$

$\dfrac{3}{4}\times \dfrac{35}{35} = \dfrac{102}{140}$

So the order will be $\displaystyle\frac{2}{7}$, $\displaystyle\frac{3}{4}$, $\displaystyle\frac{4}{5}$

Which one of the following is correct?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac {-7}{10} < \dfrac {-2}{3} < \dfrac {-5}{8}$

  2. $\dfrac {-5}{8} < \dfrac {-2}{3} < \dfrac {-7}{10}$

  3. $\dfrac {-5}{8} < \dfrac {-7}{10} < \dfrac {-2}{3}$

  4. $\dfrac {-7}{10} < \dfrac {-5}{8} < \dfrac {-2}{3}$

Show answer
Correct Option: A

Arrange in descending order:
$6,00,780;  5,56,879; 6,87,340; 4,76,980$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $4,76,980; 6,00,780; 5,56,879; 6,87,340; $

  2. $5,56,879;6,00,780; 6,87,340; 4,76,980$

  3. $ 6,87,340; 6,00,780;5,56,879; 4,76,980$

  4. $6,00,780; 6,87,340; 4,76,980; 5,56,879;$

Show answer
Correct Option: C
Explanation:

Comparing digits at lakh's place followed by ten thousand's, thousand's, hundred's, ten's and one's place,


We can arrange the given numbers in descending order as 
$6,87,340;\ 6,00,780;\ 5,56,879;\ 4,76,980$

Arrange in ascending  order:
$9,78,654;  8,78,654;  9,56,236;  9,54,234$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $9,78,654; 8,78,654; 9,56,236; 9,54,234$

  2. $ 8,78,654; 9,56,236; 9,54,234; 9,78,654$

  3. $ 8,78,654; 9,54,234; 9,56,236; 9,78,654$

  4. $ 9,54,234; 9,56,236; 9,78,654; 8,78,654$

Show answer
Correct Option: C
Explanation:

Comparing digits at lakh's place followed by ten thousand's, thousand's, hundred's, ten's and one's place,


We can arrange the given numbers in ascending order as 
$8,78,654;\ 9,54,234;\ 9,56,236;\ 9,78,654$

Arrange in ascending order:
$12,098; 12,908; 12,809; 12,890$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $12,098; 12,908; 12,809; 12,890$

  2. $12,098;12,809; 12,890; 12,908;$

  3. $12,098;12,890; 12,908; 12,809$

  4. $12,890; 12,908; 12,809; 12,098$

Show answer
Correct Option: B
Explanation:

Comparing digits at ten thousand's place followed by thousand's, hundred's, ten's and one's place,


We can arrange the given numbers in ascending order as 
$12,098; 12,809; 12,890; 12,908$

Arrange in ascending order:
$1,234; 2,345; 6,784; 1,543$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $1,234; 2,345; 6,784; 1,543$

  2. $1,234; 1,543; 2,345; 6,784$

  3. $1,543; 1,234;2,345; 6,784$

  4. $1,543; 1,234; 6,784; 2,345$

Show answer
Correct Option: B
Explanation:

Comparing digits at thousand's place followed by hundred's, ten's and one's place,


We can arrange the given numbers in ascending order as 
$1,234; 1,543; 2,345; 6,784$

Which of the following decimals are arranged in ascending order?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $0.5, 0.42, 0.382$

  2. $11.001, 11.1, 11.21$

  3. $20.3, 30.02, 23.25$

  4. $8.9, 8.86, 8.094$

Show answer
Correct Option: B
Explanation:
Ascending order means increasing the order of a series, sequence or pattern.

Option A= $0.5>0.42>0.382$ : Numbers are in descending order
Option B= $11.001<11.1<11.21$ : Numbers are in ascending order
Option C= $20.3<30.02>23.25$ : Numbers are not in proper order
Option D= $8.9>8.86>8.094$ :Numbers are in descending order.

Option $B$ is the correct answer.

Which of the following fractions are in order from the least to the greatest?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac {1}{2}, \dfrac {2}{3}, \dfrac {2}{6}$

  2. $\dfrac {1}{2}, \dfrac {2}{6}, \dfrac {2}{3}$

  3. $\dfrac {2}{6}, \dfrac {2}{3}, \dfrac {1}{2}$

  4. $\dfrac {2}{6}, \dfrac {1}{2}, \dfrac {2}{3}$

Show answer
Correct Option: D
Explanation:

First convert the given fractions into like fractions.
L.C.M. of $2, 3, 6 = 6$
So,
$\dfrac {1}{2} = \dfrac {1\times 3}{2\times 3} = \dfrac {3}{6}; \dfrac {2}{3} = \dfrac {2\times 2}{3\times 2} = \dfrac {4}{6}; \dfrac {2}{6} = \dfrac {2\times 1}{6\times 1} = \dfrac {2}{6}$
So, ascending order is,
$\dfrac {2}{6}, \dfrac {3}{6}, \dfrac {4}{6}$ i.e. $\dfrac {2}{6}, \dfrac {1}{2}, \dfrac {2}{3}$.

Smallest $6$-digit number that can be formed using $9,2,6,0,3,1$ (using each digit only once) is _________ .

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $012369$

  2. $102369$

  3. $106239$

  4. $103269$

Show answer
Correct Option: B
Explanation:

To find the smallest digit start arranging the numbers in ascending order.

However, $0$ cannot be the first or else the number would become $5$ digit.
Therefore, $102369$ is the correct answer.

Which of the following options is arranged in descending order?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $7,39,154$; $7,93,154$; $1,73,541$; $7,93,951$

  2. $8,50,76,745$; $8,50,76,547$; $8,50,67,574$; $8,50,67,547$

  3. $4,76,098$; $4,87,678$; $76,908$; $87,876$

  4. $3,15,45,001$; $3,51,54,100$; $4,15,45,001$; $5,25,45,010$

Show answer
Correct Option: B
Explanation:

The correct descending orders are


1) $7,93,951 > 7,93,154 > 7,39,154 > 1,73,541$


2) $8,50,76,745 > 8,50,76,547 > 8,50,67,574 > 8,50,67,547$

3) $4,87,678 > 4,76,098 > 87,876 > 76,908$

4) $5,25,45,010 > 4,15,45,001 > 3,51,54,100 > 3,15,45,001$

Hence option B has the correct sequence of descending order.

The ascending order of XX, XXXVI, V is ________.

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. V, XXXVI, XX

  2. XX, V, XXVI

  3. V, XX, XXXVI

  4. XXXVI, XX, V

Show answer
Correct Option: C
Explanation:

The ascending order of XX, XXXVI, V is V, XX, XXXVI

Which of the following is ninth to the right of the seventeenth from the right end of the given arrangement?

M O K T % J 9 I B @ 8 $\circledS$ C # F 1 V 7 $\Box$ 2 E G 3 Y 5 $ 6 T

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. E

  2. %

  3. I

  4. Y

Show answer
Correct Option: A
Explanation:

For the given arrangement we can see that the $17$ th no from right end is $\circledS$, 

and we can easily see that $9$ th no from the right of the $17$ th element from the right is E .

If the digits of the number $5726489$ are arranged in ascending order, then how many digits will remain at the same position?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. None

  2. One

  3. Two

  4. Three

Show answer
Correct Option: D
Explanation:

The given number is $5726489$.


After arranging digits of number in ascending order the number becomes $2456789$

Now, we can see after arranging number in ascending order digits $6,8$ and $9$ remain at the same position.

$\therefore$  $3$ digits will  remain at the same position.

Write the following rational numbers in ascending order:

$\dfrac{3}{4},\dfrac{7}{12}, \dfrac{15}{11}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{-4}{5}, \dfrac{-102}{81}, \dfrac{-13}{7}$.

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac{-13}{7},\dfrac{-102}{81}, \dfrac{-4}{5}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{15}{11}, \dfrac{7}{12}, \dfrac{3}{4}$.

  2. $\dfrac{-13}{7},\dfrac{-102}{81}, \dfrac{-4}{5}, \dfrac{7}{12}, \dfrac{3}{4}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{15}{11}$.

  3. $\dfrac{-13}{7},\dfrac{-102}{81}, \dfrac{-4}{5}, \dfrac{7}{12}, \dfrac{3}{4}, \dfrac{101}{100}, \dfrac{22}{19}, \dfrac{15}{11}$.

  4. $\dfrac{3}{4},\dfrac{7}{12}, \dfrac{15}{11}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{-4}{5}, \dfrac{-102}{81}, \dfrac{-13}{7}$.

Show answer
Correct Option: C

If the following numbers  are arranged in ascending order, what will be the middle number?
$687,\ 789,\ 648,\ 693,\ 672$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. 687

  2. 789

  3. 693

  4. 672

Show answer
Correct Option: A
Explanation:

Given numbers in ascending order is, 


$648, 672, 687, 693, 789$


It can be clearly seen that middle number is $687.$ 

Among $\dfrac{5}{6},\dfrac{5}{7}$ and $\dfrac{5}{8}$, the greatest fraction is 

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac{5}{6}$

  2. $\dfrac{5}{7}$

  3. $\dfrac{5}{8}$

  4. None of these

Show answer
Correct Option: A
Explanation:
Since all the fractions having same numarator so the greatest fraction will one with lowest denominator
 So the greatest fraction is $\dfrac{5}{6}$

Arrange in ascending order $\sqrt [ 6 ]{ 7 } ,\sqrt [ 4 ]{ 3 } ,\sqrt [ 12 ]{ 48 } $

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\sqrt [ 4 ]{ 3 } ,\sqrt [ 12 ]{ 48 } ,\sqrt [ 6 ]{ 7 } $

  2. $\sqrt [ 12 ]{ 48 } ,\sqrt [ 4 ]{ 3 } ,\sqrt [ 6 ]{ 7 } $

  3. $\sqrt [ 6]{ 7 } ,\sqrt [ 12 ]{ 48 } ,\sqrt [ 4 ]{ 3 } $

  4. $None\ of\ these$

Show answer
Correct Option: A

The ascending order of minimum values of the function  $P:\sin ^{ -1 }{ x } -\cos ^{ -1 }{ x } $, $Q=\tan ^{ -1 }{ x } -\cot ^{ -1 }{ x } $, $R=\sec ^{ -1 }{ x } -\csc ^{ -1 }{ x } $

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. P, Q, R

  2. P, R, Q

  3. Q, P, R

  4. Q, R, P

Show answer
Correct Option: A

The value of $1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$ is?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac{121}{108}$

  2. $\dfrac{3}{2}$

  3. $\dfrac{31}{2}$

  4. $\dfrac{91}{81}$

Show answer
Correct Option: D
Explanation:

$1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$


$=1+\dfrac{1}{12}+\dfrac{1}{36}+\dfrac{1}{108}+\dfrac{1}{324}$


$=\dfrac{324+27+9+3+1}{324}$

$=\dfrac{364}{324}$

$=\dfrac{91}{81}$

Hence, the answer is $\dfrac{91}{81}.$

The ascending order of $\sqrt { 2 } ,\sqrt [ 3 ]{ 4 } ,\sqrt [ 4 ]{ 6 } $ is

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\sqrt { 2 } ,\sqrt [ 3 ]{ 4 } ,\sqrt [ 4 ]{ 6 } $

  2. $\sqrt { 2 } ,\sqrt [ 4 ]{ 6 } ,\sqrt [ 3 ]{ 4 } $

  3. $\sqrt [ 3 ]{ 4 }, \sqrt {2},\sqrt [ 4 ]{ 6 } $

  4. $\sqrt [ 4 ]{ 6 },\sqrt [ 3 ]{ 4 } ,\sqrt {2}$

Show answer
Correct Option: A

Find the rational numbers between the following numbers. 

$-0.2$ and $-0.22$.

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $-0.210 > -0.211 > -0.312 > -0.213 > -0.314 > 0.220$

  2. $-0.210 > -0.211 > -0.212 > -0.213 > -0.314 > 0.220$

  3. $-0.210 > -0.211 > -0.312 > -0.213 > -0.214 > 0.220$

  4. $-0.210 > -0.211 > -0.212 > -0.213 > -0.214 > 0.220$

Show answer
Correct Option: D
Explanation:

Rational number between two numbers $ a $ and $ b = \dfrac {(a +

b)}{2} $

So, a rational number between $ -0.2 $ and $ - 0.22 = \dfrac {(-0.2 - 0.22)}{2} = -0.21 $

Now, another rational number between $ -0.21 $ and $ - 0.22 = \dfrac {(-0.21 - 0.22)}{2} = -0.215 $

rational number between $ -0.215 $ and $ - 0.21 = \dfrac {(-0.215 - 0.21)}{2} = -0.212 $ 

rational number between $ -0.215 $ and $ - 0.212 = \dfrac {(-0.215 - 0.212)}{2} = -0.213 $ 

rational number between $ -0.215 $ and $ - 0.213 = \dfrac {(-0.215 - 0.213)}{2} = -0.214 $ 

Similarly,
rational numbers between $ -0.2 $ and $ - 0.22 $ are $-0.210, -0.211 , -0.212, -0.213 , -0.214$ etc

Find the five rational numbers between $-5$ and $-6$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $-5.1 ,-5.2 , -3.3 , -5.4 , -5.5  $

  2. $-5.1 ,-5.2 , -5.3 , -5.4 , -5.5 $

  3. $-5.1 , -6.2 , -5.3 , -5.4 , -5.5 $

  4. $-6.1 , -5.2 , -5.3 , -5.4 , -5.5 $

Show answer
Correct Option: B
Explanation:
$−5>(−5−0.1)=−5.1>−5.2=(−5.1−0.1)>−5.3=(−5.2−0.1)>−5.4\\=(−5.3−0.1)>−5.5=(−5.4−0.1)>...>−6$

$-5>−5.1>−5.2>−5.3>−5.4>−5.5...>−6$

The five rational numbers between $−5$ and $−6$
$-5.1 ,-5.2 , -5.3 , -5.4 , -5.5 $

Which one is in the descending order in the following?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\displaystyle 6/7, 4/5, 3/4, 7/9$

  2. $\displaystyle 6/7, 4/5, 7/9, 3/4$

  3. $\displaystyle 3/4, 7/9, 4/5, 6/7$

  4. $\displaystyle 7/9, 3/4, 6/7, 4/5$

Show answer
Correct Option: B
Explanation:
Here we have four factors $\dfrac{3}{4},  \dfrac{4}{5},   \dfrac{6}{7},   \dfrac{7}{9}$
LCM of 4, 5, 7 and 9 is 1260
So, 
$\dfrac{3}{4} \times\dfrac{315}{315}$ = $\dfrac{945}{1260}$

$\dfrac{4}{5} \times\dfrac{252}{252}$ = $\dfrac{1008}{1260}$

$\dfrac{6}{7} \times\dfrac{180}{180}$ = $\dfrac{1080}{1260}$

$\dfrac{7}{9} \times\dfrac{140}{140}$ = $\dfrac{980}{1260}$
As, 
1080 > 1008 > 980 > 945
So, $\dfrac{6}{7} > \dfrac{4}{5} >  \dfrac{7}{9} >  \dfrac{3}{4}$

Arrange in descending order:
$1,00,000; 99,999; 9,90,000; 1,10,000$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $1,00,000; 99,999; 9,90,000; 1,10,000$

  2. $ 1,10,000; 9,90,000; 99,999; 1,00,000$

  3. $ 9,90,000; 99,999; 1,10,000; 1,00,000$

  4. $ 9,90,000; 1,10,000; 1,00,000; 99,999$

Show answer
Correct Option: D
Explanation:

Comparing digits at lakh's place followed by ten thousand's, thousand's, hundred's, ten's and one's place,


We can arrange the given numbers in descending order as 
$9,90,000;\ 1,10,000;\ 1,00,000;\ 99,999$

Arrange the following in descending order.
$\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$, $\dfrac{9}{8}$ 

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac{7}{2}$, $\dfrac{9}{8}$, $\dfrac{3}{2}$, $\dfrac{9}{5}$, $\dfrac{5}{2}$

  2. $\dfrac{7}{2}$, $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$

  3. $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$, $\dfrac{7}{2}$

  4. $\dfrac{9}{8}$, $\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$

Show answer
Correct Option: B
Explanation:

$\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2},\cfrac{9}{5},\cfrac{9}{8}$

We know that the number with largest denominator is the smallest one.
And among $\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2}$ the one with largest numerator is the largest one.
Among $\cfrac{9}{5}$ and $\cfrac{3}{2},$ $\cfrac{9}{5}$ is larger.
Hence descending order is $\cfrac { 7 }{ 2 } ,\cfrac { 5 }{ 2 } ,\cfrac { 9 }{ 5 } ,\cfrac { 3 }{ 2 } ,\cfrac { 9 }{ 8 }.$

What is the difference in the place values of the digit 8 in the number 9380568?

maths concepts of seven and eight digit numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. 79992

  2. 78992

  3. 799992

  4. 789992

Show answer
Correct Option: A
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