A student argues that 0.01% = 0.01 because in 0.01%, the percent is already written as a decimal. How do you respond?
Bogus.
1% = 0.01
because "percent" means "per 100"
1 per 100 = 1/100 = 1%
.01% means .01/100 = .0001
The student's argument is not correct. While it is true that 0.01% is written with the percent symbol, it is not already in decimal form. The percent symbol represents "per hundred," so 0.01% means 0.01 per hundred. To convert it to decimal form, we divide by 100, which gives us 0.0001. Therefore, 0.01% is equal to 0.0001, not 0.01.
To respond to the student's argument, you can explain the difference between 0.01% and 0.01. Here's how you can break it down:
1. Explain the meaning of percent: Percent is a way to express a fraction or ratio out of 100. For example, 50% means 50 out of 100, or 50/100.
2. Convert 0.01% to decimal form: To convert a percentage to a decimal, you divide it by 100. So in this case, 0.01% is written as 0.01/100, which equals 0.0001.
3. Clarify the misunderstanding: The student claims that 0.01% is equal to 0.01 because it is already written as a decimal. However, this is incorrect. While both values are decimal numbers, they represent different quantities.
4. Compare the values: When you compare 0.01% and 0.01, you'll find that 0.01 is 100 times larger than 0.01%. This is because 0.01 is equivalent to 1/100, while 0.01% is equivalent to 1/10,000. Therefore, they are not the same.
In conclusion, it's important to understand that even though a percentage may be written as a decimal, it doesn't automatically make it the same as that decimal number.