Question

If p/q form of 0.3888… is m/n then the value of (m + n) is *

Answer 1

Answer:

25. If

form of 0.38888.... is

then the value of m + n is

Answer 2

Answer:

The value of $(m + n)$ is 25.

Step-by-step explanation:

Step 1 of 4

Consider the given number as follows:

$0.3888...$

or,

$0.3\overline{8}=0.3888...$

Now, let $x=0.3\overline8$. Then,

$x=0.3888...$ ____ (1)

Step 2 of 4

Notice that the only one-digit, i.e., 8 is repeating.

So, multiply the equation (1) by the number $10$ as follows:

⇒ $10x=10\times0.3888...$

⇒ $10x=3.888...$ ____ (2)

Also, multiply the equation (1) by the number $100$ as follows:

⇒ $100x=100\times0.3888...$

⇒ $100x=38.888...$ ____ (3)

Step 3 of 4

Find the value of $x$.

Subtract the equation (2) form the equation (3) as follows:

⇒ $100x-10x=38.888... -3.888...$

⇒ $90x=35$

⇒ $x=\frac{35}{90}$

⇒ $x=\frac{7}{18}$

Thus, p/q form of the number $0.3888...$ is $\frac{7}{18}$.

Step 4 of 4

Find the value of (m + n).

Since the p/q form of the number $0.3888...$ is m/n.

From step (3), we have

$\frac{m}{n}= \frac{7}{18}$

⇒ $m = 7$ and $n = 18$

⇒ $m + n = 7 + 18$

⇒ $m + n = 25$

Final answer: The value of $(m + n)$ is 25.

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