To find the volume whose [tex]\( 16 \frac{2}{3} \% \)[/tex] is 0.75 liters, we need to understand how percentages work and apply it accordingly.
1. Convert the percentage to a decimal:
[tex]\( 16 \frac{2}{3} \% \)[/tex], which is a mix of a whole number and a fraction, can be converted to a decimal.
First, convert the fraction to a decimal:
[tex]\[ \frac{2}{3} \approx 0.6667 \][/tex]
So,
[tex]\[ 16 \frac{2}{3} \% = 16 + 0.6667 = 16.6667 \% \][/tex]
Next, convert the percentage to a decimal by dividing by 100:
[tex]\[ 16.6667 \% = \frac{16.6667}{100} = 0.166667 \][/tex]
2. Set up the problem as a proportion:
If 0.75 liters is [tex]\( 16.6667 \% \)[/tex] of some total volume [tex]\( V \)[/tex], we set up the equation:
[tex]\[ 0.166667 \times V = 0.75 \][/tex]
3. Solve for the total volume [tex]\( V \)[/tex]:
To find [tex]\( V \)[/tex], divide both sides by the decimal representation of the percentage:
[tex]\[ V = \frac{0.75}{0.166667} \][/tex]
When you perform this division, you get:
[tex]\[ V \approx 4.499991000018 \][/tex]
4. Interpret the result:
Thus, the volume [tex]\( V \)[/tex] whose [tex]\( 16 \frac{2}{3} \% \)[/tex] is 0.75 liters is approximately [tex]\( 4.499991 \)[/tex] liters (rounded to several decimal places for precision).
