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?
A percent decrease question gives you a starting amount and a smaller amount left. Subtract to find the loss, then use Desmos to divide it by the starting amount and multiply by . Compare the loss with where the quantity started, not with what remains. Using the remaining amount as the base makes the percent too large.
Hints
- Hint 1
The amount lost is the difference between the starting and remaining volumes. Subtract the volume left from the volume the flask held at first. How many liters evaporated?
- Hint 2
The base of a percent decrease is the amount before the change. Put the starting volume, not the remaining volume, under the amount lost. Then multiply that fraction by to get a percent.
Step-by-step
Compare the loss with the original volume
Step 1Find the volume lost
The flask started with liters and ended with liters. Subtract to find the amount evaporated:
- Step 2
Choose the starting volume as the base
A percent decrease measures the loss against what the flask held before evaporation. So the loss as a fraction of the original volume is
Don't divide by : that would compare the loss with what remains.
- Step 3
Convert to a percent
Multiply the fraction by to express it as a percent. Type in Desmos; it prints . To the nearest tenth of a percent, the flask's volume decreased by . Choice C.