Express each of the following in the form of pqi 0-555 -

Let x = 0.555... = 0.5 —— (1) Then, 10x = 5.555.... = 5.5 —— (2) Subtracting equation (1) from (2), we get: nbsp;10x x = 5.5 0.5 Or, 9x = 5 Or, x = 59 n ...

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Standard XII

Mathematics

Logarithmic Inequalities

Express each ...

Question

Express each of the following in the form of $\frac{p}{q}$
(i) 0.555.......

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Solution

Let x = 0.555... = $0.5$ ------ (1)
Then,
10x = 5.555.... = $5.5$ -------(2)

Subtracting equation (1) from (2), we get:
10x $-$ x = $5.5 - 0.5$
Or, 9x = 5
Or, x = $\frac{5}{9}$

So, $0.5555 . . . = \frac{5}{9}$

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Express each of the following in the form of pq (i) 0.555.......

Let x = 0.555... = 0.5 ------ (1) Then, 10x = 5.555.... = 5.5 -------(2) Subtracting equation (1) from (2), we get: 10x-x = 5.5-0.5 Or, 9x = 5 Or, x = 59 So, 0.5555...=59

Express each of the following in the form of $\frac{p}{q}$
(i) 0.555.......

Let x = 0.555... = $0.5$ ------ (1)
Then,
10x = 5.555.... = $5.5$ -------(2)

Subtracting equation (1) from (2), we get:
10x $-$ x = $5.5 - 0.5$
Or, 9x = 5
Or, x = $\frac{5}{9}$

So, $0.5555 . . . = \frac{5}{9}$