Tag: operations on rational numbers

Questions Related to operations on rational numbers

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 $\dfrac{5}{6}$