question_answer 8)

Compare the following numbers: (i) \[2.7\times {{10}^{12}};1.5\times {{10}^{8}}\]                (ii) \[4\times {{10}^{14}};3\times {{10}^{17}}\]

Answer:

                (i) \[2.7\times {{10}^{12}}=2.7\times 10\times 10\times 10\times 10\times 10\times \]\[10\times 10\times 10\times 10\times 10\] \[=2.7\times 10000\times {{10}^{8}}\] \[=27000\times {{10}^{8}}\] Clearly, \[27000\times {{10}^{8}}>1.5\times {{10}^{8}}\] \[\Rightarrow \]\[2.7\times {{10}^{12}}>1.5\times {{10}^{8}}\] (ii) \[3\times {{10}^{17}}=3\times 10\times 10\times 10\times 10\times 10\times 10\times 10\] \[\times 10\times 10\times 10\times 10\times 10\times 10\times 10\times 10\times 10\times 10\] \[=3\times 1000\times {{10}^{14}}\] \[=3000\times {{10}^{14}}\] \[\because \] \[3000\times {{10}^{14}}>4\times {{10}^{14}}\] \[\therefore \] \[3\times {{10}^{17}}>4\times {{10}^{14}}\]