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Multiple choice maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

$\displaystyle \frac{\left ( 2.3 \right )^{3}-0.027}{\left ( 2.3 \right )^{2}+0.69+0.09}=? $

  1. $2.6$
  2. $2$
  3. $2.33$
  4. $2.8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$\dfrac { { \left( 2.3 \right)  }^{ 3 }-0.027 }{ { \left( 2.3 \right)  }^{ 2 }+0.69+0.09 } \\ =\dfrac { 12.167-0.027 }{ 5.29+0.69+0.09 } \\ =\dfrac { 12.14 }{ 6.07 } \\ =2$
So, correct answer is option B.
Multiple choice maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

Which of the following is equal to $1$?

  1. $\displaystyle \frac{(0.11)^{2}}{(1.1)^{2}\times 0.1}$
  2. $\displaystyle \frac{(1.1)^{2}}{11^{2}\times (0.01)^{2}}$
  3. $\displaystyle \frac{(0.011)^{2}}{1.1^{2}\times 0.01^2}$
  4. $\displaystyle \frac{(0.11)^{2}}{1.1^{2}\times 0.01}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$\Rightarrow \cfrac{(0.11)^{2}}{(1.1)^{2}\times 0.1}=\cfrac{0.0121}{1.21\times 0.1}=\cfrac{0.0121}{0.121}=0.1$

$\Rightarrow \cfrac{(1.1)^{2}}{11^{2}\times (0.01)^{2}}=\cfrac{1.21}{121\times 0.0001}=\cfrac{0.01}{0.0001}=100$

$\Rightarrow \cfrac{(0.011)^{2}}{(1.1)^{2}\times (0.01)^{2}}=\cfrac{0.000121}{1.21\times 0.0001}=1$

$\Rightarrow \cfrac{(0.11)^{2}}{1.1^{2}\times 0.01}=\cfrac{0.0121}{1.21\times 0.01}=\cfrac{0.0121}{1.21}=1.21$