- Round the initial value 605 to 600 and the final value 203 to 200.
- Calculate the absolute decrease using the rounded values: \(600 - 200 = 400\).
- Determine the ratio of the decrease to the initial value: \(\frac{400}{600} = \frac{2}{3} \approx 0.667\).
- Convert this ratio to a percentage to find the decrease is approximately \(\boxed{66\%}\).
Explanation
- Analyzing the Problem and Applying Rounding
We are given an initial count of 605 and a final count of 203. To find the approximate percent decrease, we need to compare the change in value to the original value. The formula for the percent decrease is:
\[ \text{Percent Decrease} = \frac{\text{Initial Value} - \text{Final Value}}{\text{Initial Value}} \times 100\% \]
Rounding the numbers makes it easier to estimate. We can round 605 to 600 and 203 to 200.
- Calculating the Percent Decrease
Using the rounded values, we first calculate the absolute decrease:
\[ 600 - 200 = 400 \]
Next, we express this decrease as a fraction of the original (rounded) value:
\[ \frac{400}{600} \]
Simplifying this fraction:
\[ \frac{400}{600} = \frac{4}{6} = \frac{2}{3} \]
To convert this to a percentage, we multiply by 100%:
\[ \frac{2}{3} \times 100\% \approx 66.67\% \]
Comparing this to the provided options, it clearly matches the third option (c).
- Conclusion and Final Answer
The estimated percent decrease is approximately 66%. This corresponds to option (c). Thus, the percent decrease was approximately \(\boxed{66\%}\).
Examples
In financial contexts, estimating changes is often essential for quick decision-making. For example, if a store initially sold 605 units of a product and now sells 203, a shopkeeper might quickly estimate the decline in demand by rounding the figures to 600 and 200. Recognizing the decline is approximately 2/3, or 66%, helps the manager swiftly adjust inventory levels without needing exact precision for every calculation. This mental math approach is a fundamental skill for efficiency in business and everyday logistics.