Question

Complete the table by finding the product and the quotient of Expression 1 and Expression 2.

Write your answers in scientific notation.

Explain your method.

Answer 1

Step1. Perform multiplication and division between Expression 1 and Expression 2 and then write under column Product and Quotient respectively.

Expression 1 Expression 2 Product Quotient

$3\times {10}^4$ $1\times {10}^4$ $3\times {10}^8$ $3$

$4\times {10}^3$ $2\times {10}^2$ $8\times {10}^5$ $2\times {10}^1$

$7.7\times {10}^{-2}$ $1.1\times {10}^{-3}$ $8.47\times {10}^{-5}$ $7\times {10}^1$

$4.5\times {10}^5$ $3\times {10}^{-1}$ $13.5\times {10}^4$ $1.5\times {10}^6$

Step 2. The method used for multiplication is $(\mathrm{a}\times {10}^{\mathrm{x}})\times (\mathrm{b}\times {10}^{\mathrm{y}})=(\mathrm{a}\times \mathrm{b})\times ({10}^{\mathrm{x}}\times {10}^{\mathrm{y}})=(\mathrm{a}\times \mathrm{b})\times \left({10}^{\mathrm{x}+\mathrm{y}}\right)$

and for division is $(\mathrm{a}\times {10}^{\mathrm{x}})÷(\mathrm{b}\times {10}^{\mathrm{y}})=(\mathrm{a}÷\mathrm{b})\times ({10}^{\mathrm{x}}÷{10}^{\mathrm{y}})=(\mathrm{a}÷\mathrm{b})\times \left({10}^{\mathrm{x}-\mathrm{y}}\right)$.