10 Questions
If an item's price increases from $50 to $70, what is the percentage increase in price?
38%
What is the percentage decrease if the original price of an item is $120 and the final price after decrease is $90?
22%
A product's price decreases from $80 to $56. What is the percentage decrease in price?
35%
If a product's price decreases by 15%, what would be the new price if the original price was $200?
$180
What is the impact of percentage error on calculations involving rounding of percentages?
Decreases precision
What is the percentage error if a measurement should be 1.5 and is recorded as 1.1?
50%
If an investment was expected to yield 8% returns but only yielded 4%, what is the percentage error?
100%
In an engineering calculation, if the expected result was 150 and the actual result obtained was 120, what is the percentage error?
30%
Consider a healthcare scenario where a diagnosis should have a 90% accuracy but has an actual accuracy of 80%. What is the percentage error?
10%
If a survey expected 70% of participants to agree with a statement but only 60% actually agreed, what is the percentage error in this case?
14.29%
Study Notes
Percentage Increase and Decrease
A percentage is often used to represent proportions of quantities out of one hundred, such as the number of people who have passed an exam or the proportion of revenue generated by different regions. When dealing with percentages, two common operations are increasing and decreasing them.
Calculating Percentage Increase
To calculate the increase as a percentage, you need to know the original value and the final value after the change. The formula is simple: Increase = ((Final Value - Original Value) / Original Value) × 100.
For example, if an item costs $36 initially and then $42 after the increase, its percentage increase would be (($42-$36) / $36) × 100 = 16.67%. This means that the item has become 16.67 dollars more expensive than before.
Calculating Percentage Decrease
Similarly, to calculate the decrease as a percentage, you need to know the original value and the final value after the change. The formula for this operation is also straightforward: Decrease = ((Original Value - Final Value) / Original Value) × 100.
If an item costs $36 initially but only $31 after the decrease, its percentage decrease would be (($36-$31) / $36) × 100 = 13.89%. Here, we see that the item has become $5 cheaper than before.
Percentage Error
Percentage error can occur when dealing with percentages. This happens because arithmetic errors are often rounded off to percentages, which introduces rounding errors into calculations. For example, if a company's revenue increased from $90 million to $100 million, calculating the percentage increase might give us 11.11%, even though the actual increase was $10 million.
To avoid percentage error, it's crucial to use exact values instead of rounded numbers. Additionally, it's important not to combine different methods of computing percentage changes, such as using both ratio and proportion. In general, the precision of percentage error depends on how many decimal places you want to keep in your computation.
Learn how to calculate percentage increase and decrease using simple formulas. Understand how percentage error can occur in calculations and the importance of using exact values to avoid errors.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
