Tag: decimal numbers

Questions Related to decimal numbers

If $28052 \div 55= 1100,$ then $280.5\div 25.5 =$ ?

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $1.1$

  2. $1.01$

  3. $0.11$

  4. $11$

Show answer
Correct Option: D
Explanation:

$\displaystyle{\frac{280.5}{25.5}}$ = $\displaystyle{\frac{280.5}{25.5} \times \frac{10}{10} \times \frac{10}{10} = \frac{2805}{2.55} \times \frac{1}{100} = \frac{1100}{100}}$ = 11

Find the values of $\displaystyle \frac{0.34-0.034}{0.00\div 34}$

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $0.306$

  2. $306$

  3. $3060$

  4. $0.0306$

Show answer
Correct Option: C
Explanation:

$\displaystyle \frac{0.34-0.034}{0.0034\div 34}=\frac{0.306}{0.0001}=\frac{0.3060}{0.0001}$

$=\displaystyle \frac{3060}{1}=3060 $

The value of $\displaystyle \frac{0.25\times0.25-0.24\times0.24}{0.49}=?$

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $0.0006$

  2. $0.49$

  3. $0.01$

  4. $0.1$

Show answer
Correct Option: C
Explanation:

Given, $\displaystyle \frac {0.25\times0.25-0.24\times0.24}{0.49}$

Using the identity $a^2 - b^2 = (a+b)(a-b)$
$\therefore \displaystyle 0.25\times 0.25 - 0.24\times 0.24 = (0.25+0.24)(0.252-0.24) = (0.49)(0.01)$

Thus, $\displaystyle \frac {0.25\times0.25-0.24\times0.24}{0.49} = \frac {0.49\times 0.01}{0.49}$ = $0.01$

$\displaystyle \frac{42.31-26.43}{42.31+26.43}\div \frac{423.1-264.3}{4.231+2.643}$  is equal to 

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $\displaystyle 10^{-2}$

  2. $\displaystyle 10^{-1}$

  3. 10

  4. $\displaystyle 10^{2}$

Show answer
Correct Option: A
Explanation:

$\displaystyle \frac{42.31-26.43}{42.31+26.43}\div \frac{423.1-264.3}{4.231+2.643}$

$=\displaystyle \frac{15.88}{68.74}\div \frac{158.8}{6.874}$
$=\displaystyle \frac{15.88}{68.74}\times \frac{6.874}{158.8}=\frac{1588}{6874}\times \frac{68.74}{1588}$
= $\displaystyle \frac{68.74}{6874}=\frac{6874}{687400}=\frac{1}{100}=0.01$

Which pair of operations will make the equation below true when inserted into the blank spaces in the order shown? $\displaystyle 2\frac{3}{10} $      $1.5$  _  $2=1.8$

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $-$ and $+$

  2. $\displaystyle \times $ and $+$

  3. $+$ and $-$

  4. $\displaystyle \times $and $-$

Show answer
Correct Option: C
Explanation:

Let us first write the mixed fraction $2\dfrac {3}{10}$ in decimals as follows:


$2\dfrac { 3 }{ 10 } =\dfrac { (2\times 10)+3 }{ 10 } =\dfrac { 20+3 }{ 10 } =\dfrac { 23 }{ 10 } =2.3$

Therefore, $2\dfrac {3}{10}=2.3$

Now, add $1.5$ to $2.3$ then we get,

$2.3+1.5=3.8$

Now subtract $2$ from $3.8$ as follows:

$3.8-2=1.8$

Therefore, we have $2.3+1.5-2=1.8$

Hence, $2\dfrac { 3 }{ 10 } +1.5-2=1.8$

In the expression $24 - [ 2.4 - { 0.24 - (0.024 - x)}] = 21.8184$, the value of x is 

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $0.0024$

  2. $0.024$

  3. $0.24$

  4. $2.4$

Show answer
Correct Option: A
Explanation:

We solve the given expression as follows:


$24−\left[ 2.4−{ \left{ 0.24−\left( 0.024−x \right)  \right}  } \right] =21.8184\ \Rightarrow 24−\left[ 2.4−{ \left{ 0.24−0.024+x \right}  } \right] =21.8184\ \Rightarrow 24−\left[ 2.4−{ \left{ 0.216+x \right}  } \right] =21.8184\ \Rightarrow 24−\left[ 2.4−{ 0.216-x } \right] =21.8184$
$\Rightarrow 24−\left[ 2.184-x \right] =21.8184\ \Rightarrow 24−2.184+x=21.8184\ \Rightarrow 21.816+x=21.8184\ \Rightarrow x=21.8184-21.816\ \Rightarrow x=0.0024$

Hence, $x=0.0024$

The simplification of $\displaystyle3\overline{36}-2.\overline{05}+1\overline{33}$ is equal to

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. 2.6

  2. 2.64

  3. $\displaystyle 2.\overline{61}$

  4. $\displaystyle 2.\overline{64}$

Show answer
Correct Option: D
Explanation:

$\displaystyle 3.\overline{36}-2.\overline{05}+1.\overline{33}$


= $\displaystyle 3+0.\overline{36}-\left ( 2+0.\overline{05} \right )+1+0.\overline{33}$

= $\displaystyle 3+\frac{36}{99}-2-\frac{5}{99}+1+\frac{33}{99}$


= $\displaystyle 2+\frac{64}{99}=2+0.\overline{64}=2.\overline{64}$

Evaluate: $515.15-15.51-1.51-5.11-1.11.$

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $491.91$

  2. $419.91$

  3. $499.19$

  4. $411.19$

Show answer
Correct Option: A
Explanation:

$515.15-15.51-1.51-5.11-1.11.$

$=515.15 - (15.51 + 1.51 + 5.11 + 1.11)$
$= 515.15 - 23.24$
$=491.91$

If k is an integer and $\displaystyle \left( 0.0025 \right) \left( 0.025 \right) \left( 0.00025 \right) \times { 10 }^{ k }$ is an integer, what is the least possible value of k ?

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. -12

  2. -6

  3. 0

  4. 6

  5. 12

Show answer
Correct Option: E
Explanation:

Given expression:

 $(25 \times 10^{-4}) $ $(25 \times 10^{-3}) $$(25 \times 10^{-5}) $
$\rightarrow$ $15625 \times 10^{-12}$.
So, to make the result an integer, we must multiply by $10^{12}$
Least possible value of k should be 12. (option E)

Match the following.

Column I Column II
(i) $715+12.59+685.35=$ (P) $417.16$
(ii) $518-( 216.80 -115.96 )=$ (Q) $213.07$
(iii) $4.090+0.050+6.500=$ (R) $1412.94$
(iv) $36.050+198.05-21.03=$ (S) $10.640$
maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. (i)$\rightarrow$ (Q), (ii) $\rightarrow$ (R), (iii)$\rightarrow$ (S), (iv) $\rightarrow$ (P)

  2. (i)$\rightarrow$ (R), (ii) $\rightarrow$ (P), (iii) $\rightarrow$(S), (iv) $\rightarrow$(Q)

  3. (i)$\rightarrow$ (R), (ii)$\rightarrow$(S), (iii) $\rightarrow$ (P), (iv) $\rightarrow$ (Q)

  4. (i)$\rightarrow$ (Q), (ii) $\rightarrow$(S), (iii) $\rightarrow$ (P), (iv)$\rightarrow$(R)

Show answer
Correct Option: B
Explanation:

(I) $715+12.59+685.35=1412.94$
(II) $518-(216.80-115.96)=518-100.84=417.16$
(III) $4.090+0.050+6.500=10.640$
(IV) $36.050+198.05-21.03=213.07$.