Question

1). Express 0. 545454.... in of rational number form (p/q)
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Answer 1

Answer:

545454/1000000

Step-by-step explanation:

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545454/1000000

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Answer 2

Answer:

The number $0.545454...$ in the $p/q$ form is 6/11.

Step-by-step explanation:

Step 1 of 3

Consider the given number as follows:

$0.545454...$

or,

$0.545454... =0.\overline{54}$

Now, let $x=0.\overline{54}$. Then,

$x=0.545454...$ ____ (1)

Step 2 of 3

Notice that the two-digits 54 are repeating.

So, multiply both the sides of the equation (1) by $100$.

⇒ $100x=100\times0.545454...$

⇒ $100x = 54.545454...$ ____ (2)

Rewrite the number $54.545454...$ as follows:

⇒ $54.545454... = 54 + 0.545454...$

⇒ $54.545454...=54+x$ (Since $x=0.545454...$)

Substitute the value of $54.545454...$ in the equation (2) as follows:

⇒ $100x = 54 +x$

Step 3 of 3

Find the value of $x$.

⇒ 100x - x = 54

⇒ 99x = 54

⇒ x = $\frac{54}{99}$

⇒ x = $\frac{6}{11}$

Final answer: The number $0.545454...$ in the $p/q$ form is 6/11.

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