- Identify the conversion factor: \(1\) inch = \(2.54\) cm.
- Use unit relationships: \(1\) foot = \(12\) inches, \(1\) km = \(100,000\) cm.
- Skateboard distance: \(90 \times 12 \times 2.54 = \boxed{2,743.2} \text{ cm}\).
- Scooter distance: \(1,020 \times 2.54 = \boxed{2,590.8} \text{ cm}\).
- Bike distance: \(\boxed{4,800} \text{ cm}\).
- Go-cart distance: \(0.03 \times 100,000 = \boxed{3,000} \text{ cm}\).
Explanation
- Analysis and Conversion Factors
The problem requires converting various distances into centimeters based on a given conversion factor. The provided conversion factor is \(100\) inches = \(254\) centimeters, which simplifies to \(1\) inch = \(2.54\) centimeters. To perform the conversions, we need the following unit relationships:
- \(1\) foot = \(12\) inches.
- \(1\) kilometer = \(100,000\) centimeters.
We will apply these conversion factors to each vehicle's distance one by one.
- Calculating Skateboard Distance
The skateboard travels \(90\) feet. First, convert this distance into inches using the factor \(1\) foot = \(12\) inches:
\(90 \text{ feet} \times 12 \text{ inches/foot} = 1,080 \text{ inches}\).
Next, convert these inches into centimeters using the factor \(1\) inch = \(2.54\) centimeters:
\(1,080 \text{ inches} \times 2.54 \text{ cm/inch} = 2,743.2 \text{ cm}\).
So, the distance traveled by the skateboard is \(2,743.2 \text{ cm}\).
- Calculating Scooter Distance
The scooter travels \(1,020\) inches. Convert this distance into centimeters using the factor \(1\) inch = \(2.54\) centimeters:
\(1,020 \text{ inches} \times 2.54 \text{ cm/inch} = 2,590.8 \text{ cm}\).
So, the distance traveled by the scooter is \(2,590.8 \text{ cm}\).
- Calculating Bike Distance
The bike distance is already provided in centimeters as \(4,800\) cm. No further calculation is needed.
- Calculating Go-cart Distance
The go-cart travels \(0.03\) kilometers. Convert this distance into centimeters using the factor \(1\) kilometer = \(100,000\) centimeters:
\(0.03 \text{ km} \times 100,000 \text{ cm/km} = 3,000 \text{ cm}\).
So, the distance traveled by the go-cart is \(3,000 \text{ cm}\).
- Final Results Summary
Collecting all the results:
- Skateboard: \(2,743.2 \text{ cm}\)
- Scooter: \(2,590.8 \text{ cm}\)
- Bike: \(4,800 \text{ cm}\)
- Go-cart: \(3,000 \text{ cm}\)
The final distances in centimeters are:
- Skateboard: \(\boxed{2,743.2}\) cm
- Scooter: \(\boxed{2,590.8}\) cm
- Bike: \(\boxed{4,800}\) cm
- Go-cart: \(\boxed{3,000}\) cm
Examples
Understanding unit conversions is essential in daily life, such as when preparing a recipe, assembling furniture, or planning travel. For example, if you are building a shelf and the plans provide measurements in inches while your measuring tape is in centimeters, knowing how to accurately convert these units ensures that all parts fit correctly. Mastering these conversions allows you to work seamlessly across different measurement systems, preventing errors and ensuring precision in various construction and craft projects.