Question

the rational form of 0.08 bar is the form of p/q then find p^2 and q^2

Answer 1

Answer:

p² is 7744

q² is 980100

Step-by-step explanation:

To find :

Value of p² and q².

Solution :

We have a number 0.08 bar.

• This is rational number because this is recurring number.
• First we will find its rational form means p/q form. So,

$\implies \sf x = 0.0 \bar{8}$ -----(i)

$\implies \sf 100 \times x = 100 \times 0.88 \bar{8}$

$\implies \sf 100x = 8.8 \bar{8}$ -----(ii)

• We will subtract (i) from (ii). So,

$\implies \sf (100x) - x = (8.8 \bar{8}) - (0.0\bar{8})$

$\implies \sf 99x = 8.8$

$\implies \sf x = \dfrac{8.8}{99}$

$\implies \pmb{ \sf x = \dfrac{88}{990} }$

Rational form of 0.08 bar is 88/990 .

Thus,

• p is 88.
• q is 990 .

Now,

$\implies \sf$ p² = (88 × 88) = 7744

$\implies \sf$ q² = (990 × 990) = 980100

Therefore,

Value of p² is 7744 and q² is 980100.

Answer 2

Answer:

• p² is 7744
• q² is 980100

Step-by-step explanation:

★ Given :-

• The rational form of $\sf 0.0\bar{8}$ is in the form of $\sf{\dfrac{p}{q}}$

★ To Find :-

• Value of p² and q²

★ Solution :-

The given number is 0.08 bar.

• As it's a recurring so it's a rational number.

First we will find its rational form means p/q form.

So,

$\longrightarrow\sf x = 0.0 \bar{8} -----(i)$

$\longrightarrow \sf 100 \times x = 100 \times 0.88 \bar{8}$

$\longrightarrow \sf 100x = 8.8 \bar{8} \: ---(ii)$

Subtracting eqⁿ (1) from eqⁿ (2) we get,

$\leadsto \sf (100x) - x = (8.8 \bar{8}) - (0.0\bar{8})$

$\leadsto \sf 99x = 8.8$

$\leadsto\sf x = \dfrac{8.8}{99}$

$\longrightarrow \pink{ \underline{\boxed{ \pmb{ \bf x = \dfrac{88}{990} }}}}$

$\therefore$ Rational form of 0.08 bar is 88/990 .

Thus,

• p is 88.
• q is 990

Now, finding p²,

$\sf \longrightarrow \: {p}^{2} = {(88)}^{2} \\ \\ \sf \longrightarrow \: {p}^{2} = (88)(88) \\ \\ \sf \longrightarrow \: {p}^{2} = 88 \times 88 \\ \\ \bf \longrightarrow \: {p}^{2} = \underline{7744}$

Now, finding q²,

$\sf \longrightarrow \: {q}^{2} = {(990)}^{2} \\ \\ \sf \longrightarrow \: {q}^{2} = (990)(990) \\ \\ \sf \longrightarrow \: {q}^{2} = 990 \times 990\\ \\ \bf \longrightarrow \: {q}^{2} = \underline{980100}$

Henceforth,

$\pmb{ \sf \: \implies \underline{ \: Value \: of \: \pink{p {}^{2} } \: is \: \blue{7744 } \: and \: \purple{ {q}^{2} } \: is \: \green{980100.}}}$