Question

Express 0.99999.... in form p/q . Are you surprised by your answer .

Answer 1

Answer:

x=0.99999 ------- equation 1

Multiply the equation 1 by 10

10x=9.99999-------- equation 2

Subtracting equation 1 from equation 2 i.e equation 2- equation 1

10x-x = 9.99999-0.99999

9x=9

x=9/9

x=1

Yes, we are surprised by this answer because 0.99999 is too much near to 1. So this answer could be justified.

MARK AS BRAINLIEST

Answer 2

Answer:

To Find:-

$\large\tt{\frac{p}{q}}$ form (Rational Form) of $0.999999...$.

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Let $x$ be = $0.999999...$ , that is, $0.\overline{9}$.

As the bar is on one decimal place,

$\therefore 10x = 9.99....$

$\implies 10x = 9.\overline{9}$

(0.999... is changed into $0.\overline{9}$)

$\implies 10x = 9 + 0.\overline{9}$

(Separated $0.\overline{9}$ from $9.\overline{9}$)

$\implies 10x = 9 + x$

(As we have taken the value of $0.\overline{9}$ as x, it is now changed into x)

$\implies 10x-x = 9$

(Taken x to the Left Hand Side from the Right Hand Side)

$\implies 9x = 9$

(After Substraction, the LHS is changed into 9x)

$\implies x = \frac{9}{9}$

(Taken 9 to the RHS)

$\blue{\implies x = 1}$

(In form of $\frac{p}{q})$

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ᴛʜᴇᴀssᴀssɪɴ's OBSERVATION:-

1. Yes, we are surprised with our answer because the outcome is 1.
2. But the number that we had convert was a Terminating Decimal Number but the outcome is not in fraction.
3. After asking teacher that why it is 1, she replied that 0.999... is very close to 1, therefore 1 was the p/q form of it.
4. Therefore, the answer has an appropriate reason.