Tag: comparing numbers

Questions Related to comparing numbers

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 
$1,234; 1,543; 2,345; 6,784$