• Recalling operations on decimals - class-VI
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Recalling operations on decimals - class-VI

Description: recalling operations on decimals
Number of Questions: 23
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Tags: fractions, decimals and rational numbers decimal fractions fractions and decimal numbers decimal numbers number system decimal forms fractions and decimals decimal representation of rational numbers and operations decimals maths
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Of the numbers 0.16, $\displaystyle \sqrt{0.16}$, $\displaystyle (0.16)^{2}$ and $\displaystyle 0.1\overline{6}$ the least number is

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $\displaystyle (0.16)^{2}$

  2. $\displaystyle \sqrt{0.16}$

  3. 0.16

  4. $\displaystyle 0.1\overline{6}$

Show answer
Correct Option: A
Explanation:

0.16 = 0.16
$\displaystyle \sqrt{0.16}=0.4 $  $\displaystyle \Rightarrow 0.0256=\left ( 0.16 \right )^{2}$
$\displaystyle \left ( 0.16 \right )^{2}=0.0256 $  $\displaystyle \Rightarrow 0.0256=\left ( 0.16 \right )^{2}$
$\displaystyle 0.\overline{16}=0.1666....$  $\displaystyle \Rightarrow 0.0256=\left ( 0.16 \right )^{2}$
is the least

Compare $\displaystyle 16.1270 \Box  16.128 $

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. >

  2. =

  3. <

  4. None of these

Show answer
Correct Option: C
Explanation:

$16.128$ ia greater than $16.1270$

Hence Option C

Compare $12.1280\square 12.129$ (using >, <, =)

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. >

  2. <

  3. =

  4. none of these

Show answer
Correct Option: B
Explanation:

$12.1280 < 12.129$
since when thousandth places are compared 8 < 9

Which of the following expressions is true?  

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. 1.3749 < 1.0399

  2. 1.7908 < 1.879

  3. 1.526 < 1.2605

  4. 1.463 < 1.3902

Show answer
Correct Option: B
Explanation:

Option A =1.3749<1.03991.3749<1.0399, it should be 1.3749>1.03991.3749>1.0399

Option B=1.7908<1.8791.7908<1.879, it is true
Option C=1.526<1.26051.526<1.2605 , it should be 1.526>1.26051.526>1.2605
Option D=1.463<1.39021.463<1.3902, it should be1.463>1.39021.463>1.3902
Hence option B is the correct answer

Compare $\displaystyle 12.1280\square 12.129$ (using $\displaystyle > ,< ,=$) 

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $\displaystyle >$

  2. $\displaystyle <$

  3. =

  4. none

Show answer
Correct Option: B
Explanation:

$\displaystyle 12.1280< 12.129$

Find the greatest number
$25.356, 2.536, 253.6, 256.3$

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $25.356$

  2. $ 2.536$

  3. $ 253.6$

  4. $ 256.3$

Show answer
Correct Option: D
Explanation:
Arranging the given numbers in ascending order we get, 
$2.536, \ 25.356, \ 253.6,\ 256.3$

Hence, $256.3$ is the greatest number

Find the smallest number:
$206.3, 203.6, 206.7, 206.76$

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $206.3$

  2. $ 203.6$

  3. $ 206.7$

  4. $206.76$

Show answer
Correct Option: B
Explanation:

$206.3,203.6,206.7,206.76$


As $203.6$ has $3$ at one's place and rest have $6$, all other integral part being same, $203.6$ is smallest number.

Which one is greater:
$256.230,256.23$

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $256.230$

  2. $256.23$

  3. Both are equal

  4. none.

Show answer
Correct Option: C
Explanation:

$256.230,256.23$


Both the numbers are equal as in fractional part of number, $0$ has no value unless it is followed by a number to its right.

State true or false.
$1.51$ is larger number among $1.47$ and $1.51$
maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. True

  2. False

Show answer
Correct Option: A
Explanation:
1.511.51 is larger number among 1.47  and  1.51.
As 47 is smaller than 51.
So, given statement is true. 

The widths of two boards are $8.125$ inches and $8\dfrac {1}{8}$ inches. Which number sentence correctly compares the widths of these two boards?

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $8.125 < 8 \dfrac {1}{8}$

  2. $8.125 = 8 \dfrac {1}{8}$

  3. $8.125 > 8 \dfrac {1}{8}$

  4. None of these

Show answer
Correct Option: B
Explanation:

$8\dfrac {1}{8}$ inches = $8.125$ inches.
So, the widths of boards are equal.

Which of the following is correct?

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $0.658 > 0.732 < 0.514 < 0.813$

  2. $0.514 < 0.658 < 0.732 < 0.813$

  3. $0.813 < 0.732 < 0.658 < 0.514$

  4. $0.514 < 0.732 < 0.658 < 0.813$

Show answer
Correct Option: B
Explanation:

The correct order of is $0.514<0.658<0.732<0.813$
Hence option B is correct.

Which of the following expressions is CORRECT?

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $0.6 < 0.06$

  2. $0.66=\displaystyle\frac{5}{9}$

  3. $455 > \displaystyle\frac{11}{25}$

  4. $\displaystyle\frac{1}{6} > 0.17$

Show answer
Correct Option: C
Explanation:

(A) $0.6 > 0.06$

As we can see, LHS and RHS are same i.e. $0.6$. So, $=$ sign must be there in between. So, this statement is false.
(B) $0.66=\displaystyle\frac{66}{100}=\frac{33}{50}\neq \frac{5}{9}$
This statement is also false.
(C) $\displaystyle 455 >\frac{11}{25}=0.44$
This ststement is true.
(D) $\displaystyle\frac{1}{6}=0.166 < 0.17$
This statemnt is also false.
So, correct answer is option C.

The greatest possible decimal fraction upto four decimal places is ___________.

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $0.9900$

  2. $0.0009$

  3. $0.9000$

  4. $0.9999$

Show answer
Correct Option: D
Explanation:

Decimal fraction is a fraction which has no integral part.

$\therefore$ Greatest possible decimal fraction $= 0.9999$ Since it has $9$ at all the four decimal places.

Select the correct option which make the given expression true.
$12.5+5\displaystyle\frac{3}{8}+8\frac{1}{8}+9\frac{4}{5}+\square 2.9+15-6.88+11.08$.

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $<$

  2. $>$

  3. $=$

  4. Can't be determined

Show answer
Correct Option: B
Explanation:

We have, $\displaystyle 12.5+5\frac{3}{8}+8\frac{1}{8}+9\frac{4}{5}$

$=12.5+\dfrac{43}{8}+\dfrac{65}{8}+\dfrac{49}{5}$
$=12.5+5.375+8.125+9.8=35.8$ 
Now lets check for $2.9+15-6.88+11.08=22.1$
Since, $35.8 > 22.1$
Therefore, $ 12.5+\displaystyle 5\frac{3}{8}+8\frac{1}{8}+9\frac{4}{5} > 2.9+15-6.88+11.08$.

Which is the smallest decimal number among the following.

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $3.4$

  2. $4.4$

  3. $2.3$

  4. $2.1$

Show answer
Correct Option: D
Explanation:

The arrangement in increasing order of given numbers $2.1<2.3<3.4<4.43$

$2.1$ is the smallest among given numbers.

The least number among $\frac { 4 }{ 9 } ,\sqrt { \frac { 9 }{ 49 }  } ,0.45\quad and\quad { (0.8) }^{ 2 }$ is

maths fractions and decimals comparing and ordering of decimals more or less comparing decimals

  1. $\frac 49$

  2. $\sqrt { \frac { 9 }{ 49 } }$

  3. 0.45

  4. $(0.8)^2$

Show answer
Correct Option: A

Convert into decimal :
$\dfrac{23}{10} = $

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $2.3$

  2. $3.3$

  3. $5.6$

  4. $2.1$

Show answer
Correct Option: A
Explanation:
$\dfrac{23}{10}=2+\dfrac{3}{10}$
$=2+0.3$
$=2.3$

Compare: $12.1280 \, \square \, 12.129$  (using >, <, =)

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $>$

  2. $<$

  3. $=$

  4. None of the above

Show answer
Correct Option: B
Explanation:

The above numbers can be compared using the place value of the numbers after the decimal point.
Thus $12.1280 < 12.129$

Which of the following numbers $0.1, 0.11,$ $\displaystyle \left ( 0.11 \right )^{2},\sqrt{0.0001}$ is the greatest ?

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $0.11$

  2. $0.1$

  3. $0.11^2$

  4. None of these

Show answer
Correct Option: A
Explanation:
Consider the given numbers and find their values as follows:

$0.10\\ 0.11\\ \left( 0.11 \right) ^{ 2 }=0.11\times 0.11=0.0121\\ \sqrt { 0.0001 } =\sqrt { \dfrac { 1 }{ 10000 }  } =\sqrt { \dfrac { 1^{ 2 } }{ 100^{ 2 } }  } =\dfrac { 1 }{ 100 } =0.010$

Now from the above values we conclude that:

$0.11<0.10<0.0121<0.010$

Hence, $0.11$ is the greatest number.

Which number is greater than $\displaystyle \frac{1}{2}$?

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $0.7$

  2. $0.25$

  3. $0.48$

  4. $0.299$

Show answer
Correct Option: A
Explanation:

$\displaystyle \frac{1}{2}=0.5$
$\displaystyle 0.7> 0.5$

$\displaystyle 0.5> 0.25$
$\displaystyle 0.5> 0.48$
$\displaystyle 0.5> 0.299$
$\therefore$ option A is correct.

Find the greater number.
$256.356,256.869$

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $256.356$

  2. $256.869$

  3. Both are equal

  4. None

Show answer
Correct Option: B
Explanation:

Since the decimal $0.869$ is greater then another decimal number $0.356$ because of the fact that $869>356$.


Also since, the number before the decimals is same in the given numbers that is $256$, therefore, we conclude that $256.869>256.356$

Hence, the greater number is $256.869$.

Find the values of each of the following correct to three places of decimals, it being given that $ \sqrt{2}=1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.2360, \sqrt{6} = 2.4495$ and $\sqrt{10} = 3.162.$ 


$\dfrac{1+\sqrt{2}}{3-2\sqrt{2}}$

maths decimal forms comparing and ordering of decimals more or less comparing decimals

  1. 14.0710

  2. 24.10710

  3. 16.0213

  4. None of the above

Show answer
Correct Option: A
Explanation:
Given,

$\dfrac{1+\sqrt 2}{3-2 \sqrt 2}$

$=\dfrac{1+\sqrt 2}{\sqrt 3 \times \sqrt 3-\sqrt 2 \times \sqrt 2 \times \sqrt 2}$

$=\dfrac{1+1.4142}{1.732 \times 1.732-1.4142 \times 1.4142 \times 1.4142}$

$=14.0710$

Find the value of the following correct to three places of decimals, it being given that $ \sqrt{2}=1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.2360, \sqrt{6} = 2.4495$ and $\sqrt{10} = 3.162.$ 


$\dfrac{3-\sqrt{5}}{3+2\sqrt{5}}$

maths decimal forms comparing and ordering of decimals more or less comparing decimals

  1. 0.102

  2. 2.1102

  3. 1.1002

  4. None of the above

Show answer
Correct Option: A
Explanation:
Given,

$\dfrac {3-\sqrt 5}{3+2\sqrt{5}}$

$=\dfrac {\sqrt{3}\times \sqrt{3}-\sqrt 5}{\sqrt{3}\times \sqrt{3}+\sqrt{2}\times \sqrt{2} \times \sqrt{5}}$

$=\dfrac {1.732\times 1.732-2.2360}{1.732\times 1.732+1.4142\times 1.4142 \times 2.2360}$

$=0.102$
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