Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

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

Find the rational numbers having the following decimal expansion:

$3 . 5\overline 2$

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?

APPEARS IN

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