Question

write the decimal expansion of the following rational number without actual division
35\50
21\25
7\8​

Answer 1

$(i) = \frac{35}{50} \\ = \frac{35}{2 \times {5}^{2} } \\ = \frac{35 \times 2}{2 \times {5}^{2} \times 2} \\ = \frac{70}{ {10}^{2} } \\ = \frac{70}{100} \\ =0 .7$

$(ii) = \frac{21}{25} \\ = \frac{21}{ {5}^{2} } \\ = \frac{21 \times {2}^{2} }{ {5}^{2} \times {2}^{2} } \\ = \frac{84}{ {10}^{2} } \\ = \frac{84}{100} \\ = 0.84$

$(iii) = \frac{7}{8} \\ = \frac{7}{ {2}^{3} } \\ = \frac{7 \times {5}^{3} }{ {2}^{3} \times {5}^{3} } \\ = \frac{875}{ {10}^{3} } \\ = \frac{875}{1000} \\ = 0.875$

Hope it helps you..........