Question

a sodium hydroxide solution contains $6.9 \times 10^{-5}$ kg of sodium hydroxide. a sodium chloride solution contains $3.1 \times 10^{-7}$ kg of sodium chloride. which estimate best describes the quotient shown?\\(\frac{6.9 \times 10^{-5}}{3.1 \times 10^{-7}}\\)\
\\(\bigcirc\\) a. between 0 and 8\
\\(\bigcirc\\) b. between 100 and 300\
\\(\bigcirc\\) c. between 0 and 1

Explanation:

Step1: Simplify the coefficient

Estimate \( \frac{6.9}{3.1} \approx \frac{7}{3} \approx 2.33 \)

Step2: Simplify the powers of 10

Use the rule \( \frac{10^m}{10^n}=10^{m - n} \), so \( \frac{10^{-5}}{10^{-7}} = 10^{-5+7}=10^{2}=100 \)

Step3: Multiply the results

Multiply the coefficient and the power of 10: \( 2.33\times100 = 233 \)
233 is between 100 and 300.

Answer:

B. between 100 and 300