question_answer 8)

                Express the following numbers in standard form:                 (i) 0.0000000000085                 (ii) 0.00000000000942                 (iii) 6020000000000000                 (iv) 0.00000000837                 (v) 31860000000

Answer:

                (i) 0.0000000000085 \[0.0000000000085=\frac{85}{{{10}^{13}}}\] \[=\frac{8.5\times 10}{{{10}^{13}}}\,=\frac{8.5\times {{10}^{1}}}{{{10}^{13}}}\,=\frac{8.5}{{{10}^{13-1}}}\] \[=\frac{8.5}{{{10}^{12}}}\,\] \[=8.5\,\times {{10}^{-12}}\] (ii) 0.00000000000942 \[0.00000000000942=\frac{942}{{{10}^{14}}}\]                 \[=\frac{9.42\times {{10}^{2}}}{{{10}^{14}}}\,=\frac{9.42}{{{10}^{14-2}}}\] \[=\frac{9.42}{{{10}^{12}}}\] \[=9.42\,\times {{10}^{-12}}\] (iii) 6020000000000000 \[6020000000000000=6.02\times {{10}^{5}}\] (iv) 0.00000000837 \[0.000000000837=\frac{837}{{{10}^{11}}}\] \[\frac{8.37\times {{10}^{2}}}{{{10}^{11}}}\,=\frac{8.37}{{{10}^{11-2}}}\] \[=\frac{8.37}{{{10}^{9}}}\] \[=8.37\times {{10}^{-9}}\] (v) 31860000000 \[31860000000=3.186\times {{10}^{10}}\]