Question

MULTIPLYING AND DIVIDING IN SCIENTIFIC NOTATION

Find the product or quotient. Write your answer in scientific notation.

$(5\times {10}^{-7})\times (3\times {10}^6)$

Answer 1

Find product

$(5\times {10}^{-7})\times (3\times {10}^6)$

$=(5\times 3)\times ({10}^{-7}\times {10}^6)$ (Multiplying digits and powers simultaneously)

$=(5\times 3)\times \left({10}^{-7+6}\right)$ (Using exponent $\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}$)

$=15\times {10}^{-1}$

$=1.5\times {10}^1\times {10}^{-1}$

$=1.5\times {10}^0$

Hence, the product (in scientific notation) is $1.5\times {10}^0$ .