The value of $$0.0\overline {37} $$ where $$0.0\overline {37} $$ stands for the number $$.0373737\, . . . . . ,\,$$ is :
A.
$$\frac{{37}}{{1000}}$$
B.
$$\frac{{37}}{{990}}$$
C.
$$\frac{{1}}{{37}}$$
D.
$$\frac{{1}}{{27}}$$
Answer :
$$\frac{{37}}{{990}}$$
Solution :
The value of $$0.0\overline {37} $$ stands for the number $$0.0373737\, . . . . . = 0.037 + 0.00037 +\, . . . . .$$
$$\eqalign{
& = \frac{{37}}{{{{10}^3}}} + \frac{{37}}{{{{10}^5}}} + ..... = \frac{{37}}{{{{10}^3}}}\left[ {1 + \frac{1}{{100}} + .....} \right] \cr
& = \frac{{37}}{{{{10}^3}}}\left[ {\frac{1}{{1 - \frac{1}{{100}}}}} \right] = \frac{{37}}{{990}} \cr} $$
Releted MCQ Question on Algebra >> Sequences and Series
Releted Question 1
If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$ is equal to:
If $$a, b, c$$ are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$ are in-