Question

If 2.03=2.030303…expressed in the form p/q, where p and q are Integers and q≠0, then p+q= ?​

Answer 1

☯ GIVEN :

• $\bf {2. \bar0 \bar3}$ expressed in the form $\dfrac {p}{q}$ where p and q are integers and q≠0,

☯ TO FIND :

• The value of p+q.

➲SOLUTION :

Let

$\sf{x = 2. \bar0 \bar3\: \: \:eq (1)}$

▪By Multiplying 100 in eq(1) on both sides :

$\sf{100x = 203. \bar0 \bar3\: \: \:eq (2)}$

▪By subtracting eq (1) from eq (2) :

$:\implies{ \sf{100x -x = 203.\bar0 \bar3 -2.\bar0 \bar3 }}$

$:\implies{ \sf{99 x = 201}}$

$:\implies{ \sf{ x =\cancel{\dfrac{201}{99}}}}$

$:\implies\underline {\blue{\boxed { \bf{ x=\dfrac{67}{33} }}}}$

Here,

• p = 67 and q = 33

★Finding p+q :

$: \leadsto\sf{p + q}$

$: \leadsto\sf{67 + 33}$

$:\leadsto \underline{\huge{\boxed{ \purple{\bf{100}}}}}$

$\huge {\pink{\therefore}}$ The value of p+q is 100.