Question

Perform each unit conversion. \(\begin{array}{ll}{\text { a. } 1.4 \text { in to mm }} & {\text { b. } 116 \text { ft to cm }} \\ {\text { c. } 1845 \text { kg to lb }} & {\text { d. } 815 \text { yd to } k m}\end{array}\)

Short answer

a. 35.56 mm, b. 3535.68 cm, c. 4067.5 lb, d. 0.7457 km

Step-by-step solution

Convert inches to millimeters

To convert inches to millimeters, multiply the number of inches by 25.4, as there are 25.4 millimeters in an inch. For 1.4 inches, the calculation is: \(1.4 \times 25.4 = 35.56\) mm.

Convert feet to centimeters

To convert feet to centimeters, multiply the number of feet by 30.48, since there are 30.48 centimeters in a foot. For 116 feet, the calculation is: \(116 \times 30.48 = 3535.68\) cm.

Convert kilograms to pounds

To convert kilograms to pounds, multiply the number of kilograms by 2.20462, which is the conversion factor for kilograms to pounds. For 1845 kilograms, the calculation is: \(1845 \times 2.20462 = 4067.5049\) lb.

Convert yards to kilometers

To convert yards to kilometers, multiply the number of yards by 0.0009144, as there are 0.0009144 kilometers in a yard. For 815 yards, the calculation is: \(815 \times 0.0009144 = 0.745676\) km.

Key concepts

Metric Conversion

Understanding metric conversion is essential in chemistry and many other scientific fields. It involves changing a measurement from one unit to another within the metric system, which is used worldwide due to its simplicity and standardization. The metric system is a decimal-based system of measurement, which means it is based on powers of ten. For instance, when converting from a smaller unit to a larger unit, you divide by factors of ten and multiply when going from larger to smaller units. For example, to convert from inches to millimeters, as shown in the exercise, you multiply by 25.4 because one inch is equivalent to 25.4 millimeters.

To solidify this understanding, let's revisit the conversion from inches to millimeters with an easy-to-follow equation: \( 1.4 \text{ inches} \times 25.4 \frac{\text{mm}}{\text{inch}} = 35.56 \text{ mm} \) This calculation shows the straightforward nature of metric conversions when you know the conversion factor.

Dimensional Analysis

Dimensional analysis, also known as the factor-label method or unit factor method, is a problem-solving strategy used to convert a given set of units to another. It involves the use of conversion factors, which are ratios that express how one unit of measurement is related to another. By arranging these conversion factors so that unwanted units cancel out, you can neatly convert from one system of measurement to another. This is particularly useful in chemistry, where precise measurements are paramount.

Take the conversion of feet to centimeters; the step-by-step solution shows how dimensional analysis works with the conversion factor: \( 116 \text{ ft} \times 30.48 \frac{\text{cm}}{\text{ft}} = 3535.68 \text{ cm} \) The feet cancel out, leaving you with centimeters, which is the desired unit. Dimensional analysis ensures accuracy in scientific calculations and helps prevent errors due to the unit confusion.

Units of Measurement

Units of measurement are the building blocks used to quantify and describe the physical properties of matter and energy. In the realm of chemistry, understanding and using the correct units is vital, as they define the scale and magnitude of what is being measured. The International System of Units (SI) is the standard adopted by scientists, which includes units like meters (m) for length, kilograms (kg) for mass, and seconds (s) for time. However, non-SI units, such as inches or feet, are still widely used in some countries and contexts.

For the conversion of kilograms to pounds provided in the steps, the concept of these units is clearly illustrated: \( 1845 \text{ kg} \times 2.20462 \frac{\text{lb}}{\text{kg}} = 4067.5049 \text{ lb} \) It’s important to note that consistency in units within a calculation is critical, and selecting the appropriate unit can make the interpretation of results significantly clearer. Units serve as the language through which scientists communicate their findings, ensuring that their measurements can be reproduced and validated globally.