Questions: An active ingredient is 6.273% of a solution. Which of the following is the fraction of the ingredient in the solution? 3 / 50 3 / 20 2 / 3 1 / 15

$An active ingredient is 6.273% of a solution. Which of the following is the fraction of the ingredient in the solution? 3 / 50 3 / 20 2 / 3 1 / 15$

Transcript text: An active ingredient is $6.273\%$ of a solution. Which of the following is the fraction of the ingredient in the solution? $3 / 50$ $3 / 20$ $2 / 3$ $1 / 15$

Solution

Solution Steps

Step 1: Convert the percentage to a decimal

The given percentage of the active ingredient is $6.273\%$. To convert this to a decimal, divide by 100: \[ 6.273\% = \frac{6.273}{100} = 0.06273 \]

Step 2: Compare the decimal to the given fractions

Now, compare the decimal $0.06273$ to the decimal equivalents of the given fractions: \[ \frac{3}{50} = 0.06, \quad \frac{3}{20} = 0.15, \quad \frac{2}{3} \approx 0.6667, \quad \frac{1}{15} \approx 0.0667 \]

Step 3: Identify the closest fraction

The decimal $0.06273$ is closest to $\frac{1}{15} \approx 0.0667$. Therefore, the fraction of the ingredient in the solution is $\frac{1}{15}$.