Express 0-123 as a rational number in the form pq- where p and q are integers and q - 0-

Let #160;x=0.1232323 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160;...(i) #8756; #160;10x=1.23232323 #160; #1 ...

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Standard IX

Mathematics

Irrational Numbers

Express 0.123...

Question

Express $0.123$ as a rational number in the form $\frac{p}{q}$ , where p and q are integers and q ≠ 0.

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Solution

$Let x = 0.1232323 . . . (i) ∴ 10 x = 1.23232323 . . . (ii) Also, 1000 x = 123.232323 . . . (iii) Subtracting (ii) from (iii), we get : 990 x = 122 \Rightarrow x = \frac{122}{990} = \frac{61}{495}$

Thus, we have:
$0.123 = \frac{61}{495}$

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Express 0.123 as a rational number in the form pq, where p and q are integers and q ≠ 0.

Let x=0.1232323 ...(i)∴ 10x=1.23232323 ...(ii)Also,1000x=123.232323 ...(iii)Subtracting (ii) from (iii), we get:990x=122⇒x=122990=61495 Thus, we have: 0.123=61495

Express $0.123$ as a rational number in the form $\frac{p}{q}$ , where p and q are integers and q ≠ 0.

$Let x = 0.1232323 . . . (i) ∴ 10 x = 1.23232323 . . . (ii) Also, 1000 x = 123.232323 . . . (iii) Subtracting (ii) from (iii), we get : 990 x = 122 \Rightarrow x = \frac{122}{990} = \frac{61}{495}$

Thus, we have:
$0.123 = \frac{61}{495}$