1.

Write the following numbers p/q in formi. 9.315315….. ii. 357.417417…..

Answer»

i.  Let x = 9.315315 … = \(9.\overline{315}\) …(i) 

Since, three numbers i.e. 3, 1 and 5 are repeating

after the decimal point. 

Thus, multiplying both sides by 1000, 

1000x = 9315.315315…

∴ 1000x =\(9315.\overline{315}\)...(ii)

Subtracting (i) from (ii)

∴ 1000x - x =\(9315.\overline{315}\) - \(9.\overline{315}\)

∴  999x = 9306

∴  \(x=\frac{9306}{999}\) = \(\frac{9\times1034}{9\times111}\) = \(\frac{1034}{111}\) 

∴  9.315315... = \(\frac{1034}{111}\) 

ii.  Let x = 357.417417…= \(357.\overline{417}\) ...(i)

Since, three numbers i.e. 4, 1 and 7 are repeating after the decimal point. 

Thus, multiplying both sides by 1000, 

1000x = 357417.417417… 

∴ 1000x = 357417.417 …(ii) 

Subtracting (i) from (ii), 

1000x – x =\(357417.\overline{417}\) - \(357.\overline{417}\) 

∴ 999x = 357060

∴ \(x=\frac{357060}{999}\) = \(\frac{3\times119020}{3\times333}\) 

∴ 357.417417... = \(\frac{119020}{333}\)



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