Question

Express the following decimals into rational form (p/q, q#0)​

Answer 1

Answer:

${ \sf{ \red{(i) \: 0.333.....}}}$

${ \to{ \sf{10x = 3.33333......}}}$

${ \to{ \sf{ \: \: x = 0 .3333.....}}}$

(-)-------------------------

${ \to{ \sf{9x = 3}}}$

${ \to{ \sf{x = \frac{3}{9} }}}$

${ \to{ \sf{x = \frac{1}{3} }}}$

${ \sf{ \red{(ii)0.535353.....}}}$

${ \to{ \sf{100x = 53.535353.....}}}$

${ \to{ \sf{x = 0.535353....}}}$

(-)---------------------------

${ \to{ \sf{99x = 53}}}$

${ \to{ \sf{x = \frac{53}{99} }}}$

${ \sf{ \red{(iii)3.5555....}}}$

${ \to{ \sf{10x = 53.333....}}}$

${ \to{ \sf{x = 5.3333......}}}$

(-) ---------------------------

${ \to{ \sf{9x = 48}}}$

${ \to{ \sf{x = \frac{48}{9} }}}$

${ \to{ \sf{x = \frac{16}{3} }}}$

${ \sf{ \red{(iv)4.6666.....}}}$

${ \to{ \sf{10x = 46.6666.....}}}$

${ \to{ \sf{x = 4.6666....}}}$

(-) ---------------------------

${ \sf{ \to{9x = 42}}}$

${ \to{ \sf{x = \frac{42}{9} }}}$

${ \sf{ \to{x = \frac{14}{3} }}}$

${ \sf{ \red{(v)0.9999.....}}}$

${ \to{ \sf{10x = 9.9999.....}}}$

${ \to{ \sf{x = 0.999......}}}$

(-)-------------------------------

${ \sf{ \to{9x = 9}}}$

${ \sf{ \to{x = \frac{9}{9} = 1}}}$

${ \sf{ \red{(vi)2.234444......}}}$

${ \to{ \sf{10x = 22.344444.....}}}$

${ \to{ \sf{x = 2.234444.....}}}$

(-) ---------------------------

${ \to{ \sf{9x = 20.11}}}$

${ \sf{ \to{x = \frac{20.11}{9} }}}$

${ \to{ \sf{ \frac{2011}{900} }}}$

Answer 2

Answer:

(I) 1/3

(ii) 53/99

(iii) 16/3

(iv) 14/3

(v) 1

(vi) 2011/900