Isabel says that 0.02 can be expressed as 20%. Is she correct? Explain why or why not.
The Correct Answer and Explanation is:
No, Isabel is incorrect in stating that 0.02 can be expressed as 20%. Here’s the correct explanation:
To express a decimal number as a percentage, you multiply the decimal by 100 and then add the percent symbol (%). This is the standard way of converting a decimal into a percentage.
Let’s break down the conversion of 0.02 into a percentage:
- Starting with 0.02:
- You multiply 0.02 by 100 to convert it to a percentage:
[
0.02 \times 100 = 2
]
- Result: The result is 2, so 0.02 is equivalent to 2%, not 20%.
Isabel’s mistake comes from misunderstanding the multiplication step. If she were to multiply by 1000, she would get 20, but this would be incorrect because multiplying by 1000 converts the decimal into a thousandths place, not a percentage. To convert a decimal to a percentage, only multiplying by 100 is required.
Key Concept: A percentage is a way of expressing a number as a fraction of 100. The formula for converting a decimal to a percentage is:
[
\text{Percentage} = \text{Decimal} \times 100
]
In summary, 0.02 is equal to 2% because multiplying it by 100 gives 2. Isabel mistakenly multiplied by 1000 or misinterpreted the process. Therefore, 0.02 cannot be expressed as 20%.