Question

Evaluate the expression. Write your answer in scientific notation.
$(4.2\times {10}^8)+(5.9\times {10}^9)$

Answer 1

Evaluating the expression

$(4.2\times {10}^8)+(5.9\times {10}^9)$

$={10}^8\times (4.2+(5.9\times 10)$ (Taking ${10}^8$ as common)

$={10}^8\times (4.2+59)$

$={10}^8\times (63.2)$ (Adding the digits in the bracket)

$={10}^8\times 6.32\times {10}^1$

$=6.32\times {10}^1\times {10}^8$

$=6.32\times {10}^{1+8}$ (Using exponent law ${\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}}$)

$=6.32\times {10}^9$ (Writing your answer in scientific notation)

Hence, the expression is $(4.2\times {10}^8)+(5.9\times {10}^9)=6.32\times {10}^9$.