Question 17·Medium·Percentages
A laboratory flask initially contained liters of a chemical solution. After several hours, some of the liquid had evaporated, and only liters remained.
To the nearest tenth of a percent, by what percent did the volume of the solution decrease?
For percent increase or decrease questions, always follow the same quick pattern: (1) subtract to find the change, (2) divide by the original amount (not the final), and (3) multiply by 100 to convert to a percent and apply any requested rounding. Keeping the original value in the denominator and doing the operations in this fixed order helps you avoid common mistakes with percent change.
Hints
Focus on the change in volume
Start by finding how many liters of solution were lost. What operation should you use with liters initially and liters remaining?
Set up the percent decrease
Percent decrease is (amount of decrease) divided by (original amount). Which number goes in the denominator: or ?
Turn a decimal into a percent
Once you have the decimal form of the decrease (for example, something like ), how do you convert that decimal into a percent, and how do you write it to the nearest tenth of a percent?
Desmos Guide
Compute the percent decrease directly
In Desmos, type the expression (2.50 - 2.15) / 2.50 * 100 and look at the numerical output. Then write that value as a percent rounded to the nearest tenth of a percent.
Step-by-step Explanation
Find how much volume was lost
The percent decrease is based on how much the volume changed.
Subtract the final amount from the original amount:
So, liters of solution evaporated.
Express the loss as a fraction of the original
Percent decrease uses the original amount in the denominator.
Set up the fraction:
Now divide:
So the volume decreased by of the original amount (in decimal form).
Convert the fraction to a percent and round
To convert a decimal to a percent, multiply by :
This is exactly . Written to the nearest tenth of a percent, this is , which matches answer choice C) 14.0%.