Question

Please help:

$\sf \dfrac{0.83\div 7.5}{2.3\overline{21}-0.0\overline{98}}$

Answer 1

★Concept:-

Here in the given question, we asked to simplify a problem but we can see that numerator is a repeating decimal value so firstly we have to make it into a non-repeating or in the fractional form so that we can simply it further.

★Solution:-

•Denominator consists of:

$\sf 2.3\overline{21}-0.0\overline{98}$

Simplifying both the terms seperately.

$\leadsto\sf 2.3\overline{21}$

Let us assume $\sf 2.3\overline{21}=x\dashrightarrow Eq.1$

Assume it as Eq.1

Multiplying Eq.1 with 10 on both LHS and RHS.

$:\implies\sf 10\times( 2.3\overline{21})=(x)\times 10$

$:\implies\sf 23.\overline{21}=10x\dashrightarrow Eq.2$

Assume it as Eq.2

Now multiplying Eq.2 by 100 on both sides.

$:\implies\sf 100\times( 23.\overline{21})=( 10x)\times100$

$:\implies\sf 2321.\overline{21}=1000x \dashrightarrow Eq.3$

Assume it as Eq.3

Now subtracting Eq.2 from equation Eq.3.

$:\implies\sf 2321.\overline{21}-23.\overline{21}=1000x -10x$

$:\implies\sf 2298=990x$

$:\implies\sf\dfrac{ 2298}{990}=x$

$\underline{\boxed{:\implies\sf\dfrac{ 385}{165}=x}}$

$\leadsto\sf 0.0\overline{98}$

Let us assume$\sf 0.0\overline{98}=y$

Multiplying this equation by 10 on both sides

$:\implies\sf (0.0\overline{98})\times 10=(y)\times10$

$:\implies\sf 0.\overline{98}=10y \dashrightarrow Eq.4$

Assume it as equation 4.

Now multiplying this equation by 100 on both sides.

$:\implies\sf (0.\overline{98})\times100=(10y)\times 100$

$:\implies\sf 98.\overline{98}=1000y\dashrightarrow Eq.5$

Assume it as Eq. 5

Now Subtracting Eq. 4 from Eq.5

$:\implies\sf 98.\overline{98}-0.\overline{98}=1000y-10y$

$:\implies\sf 98=990y$

$:\implies\sf \dfrac{98}{990}=y$

$\underline{\boxed{:\implies\sf \dfrac{49}{495}=y}}$

Now we have obtained both values of denominator in the form of x and y.

Put them in the given equation.

$\sf :\implies\dfrac{0.83\div 7.5}{2.3\overline{21}(x)-0.0\overline{98}(y)}$

$\sf :\implies\dfrac{0.83\div 7.5}{\bigg(\dfrac{383}{165}-\dfrac{49}{495}\bigg)}$

$\sf :\implies\dfrac{\bigg(\dfrac{0.83}{7.5}\bigg)}{\bigg(\dfrac{1149-49}{495}\bigg)}$

$\sf :\implies\dfrac{\bigg(\dfrac{83\times 10}{75\times 100}\bigg)}{\bigg(\dfrac{1100}{495}\bigg)}$

$\sf :\implies\dfrac{\bigg(\dfrac{83\times 1\not 0}{75\times 10\not 0}\bigg)}{\bigg(\dfrac{1100}{495}\bigg)}$

$\sf :\implies\dfrac{\bigg(\dfrac{83}{750}\bigg)}{\bigg(\dfrac{1100}{495}\bigg)}$

$\sf :\implies\dfrac{83\times 495}{75\times 11000}$

$\Large\underline{\boxed{\sf{\red{ :\implies 0.0498}}}}$

$\textsf{So the final answer is 0.0498}$

Answer 2

Answer:

Lions are considered as the king of the jungle because they are durable and have a high hunting capacity. The hungry animal has four legs and a tail with healthy paws. Mane is the name of the hair that is on the lion's neck. Lions are carnivorous animals, which is when animals hunt and eat the flesh of other animals.

Step-by-step explanation:

hope you are understand