Question

Perform each conversion. (a) \(40.0 \mathrm{~cm}\) to inches (b) \(27.8 \mathrm{~m}\) to feet (c) \(10.0 \mathrm{~km}\) to miles (d) \(3845 \mathrm{~kg}\) to pounds

Short answer

a) 15.748 inches, b) 91.207 feet, c) 6.21371 miles, d) 8477.3779 pounds

Step-by-step solution

Convert centimeters to inches

To convert centimeters to inches, use the conversion factor 1 inch = 2.54 centimeters. Divide the number of centimeters by 2.54 to get the number of inches. Calculation: \( \frac{40.0 \text{ cm}}{2.54 \text{ cm/in}} = 15.748 \text{ inches} \).

Convert meters to feet

To convert meters to feet, use the conversion factor 1 meter = 3.28084 feet. Multiply the number of meters by 3.28084 to get the number of feet. Calculation: \( 27.8 \text{ m} \times 3.28084 \text{ ft/m} = 91.207 \text{ feet} \).

Convert kilometers to miles

To convert kilometers to miles, use the conversion factor 1 kilometer = 0.621371 miles. Multiply the number of kilometers by 0.621371 to get the number of miles. Calculation: \( 10.0 \text{ km} \times 0.621371 \text{ mi/km} = 6.21371 \text{ miles} \).

Convert kilograms to pounds

To convert kilograms to pounds, use the conversion factor 1 kilogram = 2.20462 pounds. Multiply the number of kilograms by 2.20462 to get the number of pounds. Calculation: \( 3845 \text{ kg} \times 2.20462 \text{ lb/kg} = 8477.3779 \text{ pounds} \).

Key concepts

Metric to Imperial Conversion

Understanding how to convert between metric and imperial units is crucial when dealing with international data or working in scientific environments.
In essence, metric to imperial conversion requires the knowledge of the proper conversion factors. Many students start by memorizing these essential constants, although it's often more practical to understand their conceptual basis.
For example, as seen in the exercise, to convert centimeters to inches, a conversion factor of 1 inch equals 2.54 centimeters is used. This factor is derived from the legal definition of an inch as exactly 2.54 cm. Similarly, for larger distances, factors such as 1 kilometer being equivalent to 0.621371 miles are used, reflecting the different scales of measurement in the two systems.

Common Conversion Factors

• 1 inch = 2.54 centimeters (for length)
• 1 foot = 0.3048 meters (for length)
• 1 mile = 1.60934 kilometers (for length)
• 1 pound = 0.453592 kilograms (for mass)

With these factors, you'll often either multiply or divide to convert from metric to imperial, depending on the direction of the conversion. It's important to practice these conversions regularly to improve your fluency in moving between the two systems.

Length Unit Conversion

When it comes to length unit conversions, the basic idea is to use a conversion factor to transition from one unit of measurement to another.
In the provided exercise steps, the conversion factor between centimeters and inches (1 inch = 2.54 centimeters) and between meters and feet (1 meter = 3.28084 feet) are practical examples. A similar approach is employed for converting kilometers to miles.

Steps for Conversion

To ensure accurate length conversions, always follow these steps:

• Identify the correct conversion factor.
• If going from a smaller to a larger unit, divide.
• If going from a larger to a smaller unit, multiply.
• Carry out the operation to obtain the result.
• Keep track of your units to avoid confusion.

Accuracy is vital, so use precise conversion factors and pay attention to significant figures, especially in chemistry, where precision can greatly impact the outcome.

Mass Unit Conversion

For mass unit conversion in a chemistry context, the situation is akin to that of length: a conversion factor is vital.
The exercise showcased converting kilograms to pounds, using a conversion factor that one kilogram equals 2.20462 pounds. This is particularly important in chemistry, where mass can affect substance quantities in reactions and product yields.

Key Tips for Accurate Mass Conversions

• Always start with the known mass and the appropriate conversion factor.
• Multiply if you're converting from a smaller to a larger unit in the imperial system, such as grams to pounds.
• Conversely, divide if you're converting from a larger to a smaller unit, such as kilograms to ounces.
• Ensure that your conversion factor is precise to maintain the integrity of your results.
• Mind the significant figures to accurately report the results in scientific contexts.

With consistent practice, these steps become second nature, enabling you to focus more on the chemistry problem at hand rather than the conversion process.

Chemistry Problem Solving

Solving chemistry problems effectively requires a logical and methodical approach, often involving unit conversions as part of the process.
It's not just about using the correct conversion factors and computations; understanding the context and what the problem requires is just as essential. This often involves identifying the given data, determining the required units for the answer, and using the right conversion factors to guide your calculations.

Effective Chemistry Problem-Solving Strategies

• Read the problem carefully and note all the given information.
• Determine what you are trying to find.
• Identify the relevant chemical principles and formulas.
• Convert all quantities to the needed units using the proper conversion factors.
• Use stoichiometry if the problem involves chemical reactions and quantities.
• Apply the appropriate formulas and carry out the calculations with care.
• Check your work for accuracy and plausibility before finalizing your answer.

By integrating unit conversion skills into your chemistry problem-solving toolset, you'll be better prepared to tackle varied and complex questions with confidence.