A store advertises 150% of its usual stock. A student says this is impossible because percents cannot exceed 100. Who is right?
AThe student — percents represent parts of a whole, so they max out at 100%
BThe store — 150% is valid and means the stock is 1.5 times the usual amount
CNeither — percents only go up to 100% but can never exceed it in commerce
DThe student — only decimals can represent values greater than 1
Percents can exceed 100. 150% simply means 150 per 100, or 1.5 times the reference value. The misconception comes from thinking of percent as always a 'part of a whole' capped at 100, but percent is a ratio that scales to any value.
Question 2 True / False
If a jacket is '30% off,' the discount amount is generally $30.
TTrue
FFalse
Answer: False
Percent is always relative to a base (the original price). 30% off a $200 jacket is $60; 30% off a $50 jacket is $15. The '$30' figure only applies if the original price happened to be $100. This is one of the most common real-world misconceptions about percents.
Question 3 Short Answer
Explain in your own words why 25%, 1/4, and 0.25 all represent the same quantity.
Think about your answer, then reveal below.
Model answer: All three represent the same fraction of a whole: 25 out of 100. Percent means 'per hundred,' so 25% = 25/100. Simplifying 25/100 gives 1/4. Dividing 25 by 100 (or 1 by 4) gives the decimal 0.25. They are three notations for the same ratio.
Understanding this equivalence is the foundation of converting between forms. Percent, fraction, and decimal are not different quantities — they are different ways of expressing the same proportional relationship.