Tag: writing and expanding numbers

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Multiple choice 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

Find the rational numbers between the following numbers. 

$-0.2$ and $-0.22$.

  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. $-0.210 > -0.211 > -0.212 > -0.213 > -0.214 > 0.220$
Reveal answer Fill a bubble to check yourself
D Correct answer
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

Multiple choice 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

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

  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 $
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $
Multiple choice 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

Which one is in the descending order in the following?

  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. $\displaystyle 7/9, 3/4, 6/7, 4/5$
Reveal answer Fill a bubble to check yourself
B Correct answer
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, $\dfrac{6}{7} > \dfrac{4}{5} >  \dfrac{7}{9} >  \dfrac{3}{4}$

Multiple choice 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

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

  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$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 
$9,90,000;\ 1,10,000;\ 1,00,000;\ 99,999$

Multiple choice 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

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

  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. $\dfrac{9}{8}$, $\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $\cfrac { 7 }{ 2 } ,\cfrac { 5 }{ 2 } ,\cfrac { 9 }{ 5 } ,\cfrac { 3 }{ 2 } ,\cfrac { 9 }{ 8 }.$