Question

ADDING AND SUBTRACTING IN SCIENTIFIC NOTATION

Find the sum or difference.

$(9.7\times {10}^6)+(6.7\times {10}^5)$

Answer 1

Taking ${10}^5$ as common factor from the given expression we get,

$(9.7\times {10}^6)+(6.7\times {10}^5)$

$={10}^5\times (9.7\times 10+(6.7)$

$={10}^5\times (97+(6.7)$

$={10}^5\times 103.7$ (Solving addition in the bracket)

$={10}^5\times 1.037\times 100$

$={10}^5\times 1.037\times {10}^2$

$=1.037\times {10}^2\times {10}^5$ ( using exponent law ${\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}}$)

$=1.037\times {10}^7$ ( Writing the number as scientific notation)