(d) $0.14189189189….$

$ = 0.14 + 0.00189 + 0.00000189 + …….$

$ = \frac{{14}}{{100}} + 189\left[ {\frac{1}{{{{10}^5}}} + \frac{1}{{{{10}^8}}} + ….\infty } \right]$

$ = \frac{7}{{50}} + 189\,\left[ {\frac{{1/{{10}^5}}}{{1 – (1/{{10}^3})}}} \right]$$ = \frac{7}{{50}} + 189\,\left[ {\frac{1}{{{{10}^5}}} \times \frac{{{{10}^3}}}{{999}}} \right]$

$ = \frac{7}{{50}} + \frac{{189}}{{999 \times 100}}$

$ = \frac{7}{{50}} + \frac{7}{{3700}} = \frac{7}{{50}} + \frac{7}{{25 \times 148}}$$ = \frac{{21}}{{148}}$.