Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

Find the Rational Numbers Having the Following Decimal Expansion: 3 . 5 ¯¯¯ 2 - Mathematics

Find the rational numbers having the following decimal expansion: 

\[3 . 5\overline 2\]

Advertisement Remove all ads

Solution

\[ 3 . 5\overline 2\]

\[\text { Let } S = 3 . 5\overline 2\]

\[ \Rightarrow S = 3 . 5 + 0 . 02 + 0 . 002 + 0002 + 0 . 00002 + . . . \infty \]

\[ \Rightarrow S = 3 . 5 + 0 . 02\left( 1 + {10}^{- 1} + {10}^{- 2} + {10}^{- 3} + {10}^{- 4} + . . . \infty \right)\]

\[\text { It is a G . P } . \]

\[ \therefore S = 3 . 5 + 0 . 02\left( \frac{1}{1 - {10}^{- 1}} \right)\]

\[ \Rightarrow S = 3 . 5 + \frac{0 . 2}{9}\]

\[ \Rightarrow S = \frac{317}{90}\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Exercise 20.4 | Q 8.3 | Page 40
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×