Question

e) \frac{(3.5 \times 10^{-4})}{(7 \times 10^{-3})}

Explanation:

Step1: Separate coefficients and exponents

We can rewrite the expression as the quotient of the coefficients times the quotient of the powers of 10: $\frac{3.5}{7} \times \frac{10^{-4}}{10^{-3}}$

Step2: Calculate the coefficient quotient

$\frac{3.5}{7} = 0.5$

Step3: Calculate the exponent quotient

Using the rule $a^m / a^n = a^{m - n}$, we have $\frac{10^{-4}}{10^{-3}} = 10^{-4 - (-3)} = 10^{-1}$

Step4: Multiply the results

Multiply the coefficient result and the exponent result: $0.5 \times 10^{-1}$

Step5: Convert to proper scientific notation

$0.5 \times 10^{-1} = 5 \times 10^{-2}$ (since $0.5 = 5 \times 10^{-1}$, so $5 \times 10^{-1} \times 10^{-1} = 5 \times 10^{-2}$)

Answer:

$5\times10^{-2}$ (or 0.05)