To analyze Sila's conversion from kilometers to feet, let's break down the units properly.
- Sila jogged 12 kilometers.
- To convert kilometers to miles, the conversion factor is approximately 0.621371 miles in 1 kilometer. Sila used 0.62, which is incorrect, but not significantly off.
- To convert miles to feet, the conversion factor is 5280 feet in 1 mile.
The correct calculation should be:
\[ 12 \text{ kilometers} \times \frac{0.621371 \text{ miles}}{1 \text{ kilometer}} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \]
However, Sila performed her calculation as follows without recognizing the necessary conversions correctly:
\[ 12 \text{ kilometers} \times \frac{0.62 \text{ miles}}{1 \text{ kilometer}} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \]
The first potential error was the choice of 0.62 instead of the more accurate 0.621371 for miles per kilometer, which leads to a slight overestimate in the result.
For the other options:
- "Sila put a wrong number in her calculator when multiplying the numerators." This could relate to how she applied the conversion factors, but as written, it is a bit vague.
- "Sila’s first fraction should be \( \frac{1 \text{ kilometer}}{0.62 \text{ miles}} \)." This statement suggests an inverse relationship that is not how conversions work in this scenario.
- "Sila’s last fraction should be \( \frac{1 \text{ mile}}{5280 \text{ feet}} \)." This statement is incorrect because the conversion from miles to feet is accurately given as \( \frac{5280 \text{ feet}}{1 \text{ mile}} \).
- "Sila forgot to divide by 0.62." This implies a misunderstanding of the conversion; it should have been multiplied, not divided.
In conclusion, the primary error Sila made in her conversion was using an incorrect value for the miles per kilometer conversion, which was approximated as 0.62 instead of using the more precise 0.621371. Therefore, the most accurate statement regarding her mistake is that she used an inaccurate conversion factor, leading to a slight misestimate in total feet traveled.
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