Carry out the following conversions: (a) \(70 \mathrm{~kg}\), the average weight of a male adult, to pounds. (b) 14 billion years (roughly the age of the universe) to seconds. (Assume there are 365 days in a year.) (c) \(7 \mathrm{ft} 6 \mathrm{in},\) the height of the basketball player \(\mathrm{Yao}\) Ming, to meters. (d) \(88.6 \mathrm{~m}^{3}\) to liters.

Understanding metric to imperial conversion is essential for solving a variety of real-world problems, such as interpreting a person's weight or comparing heights in different unit systems. The metric system uses units like kilograms for mass and meters for length, while the imperial system uses pounds and feet/inches respectively.

To convert from metric to imperial, one needs to know the right conversion factors. For instance, in the textbook solution for converting the average weight of an adult from kilograms to pounds, the conversion factor of 1 kg equals approximately 2.20462 pounds is used. By simply multiplying the given value in the metric system by this factor, the result is obtained in the imperial system.

• Multiply the metric value by the conversion factor to get the imperial value.
• Conversion factors are specific to the type of measurement, e.g., mass, length, or volume.
• Unit consistency is key—an incorrect conversion factor can lead to inaccurate results.

Time unit conversion can often involve large numbers, especially when dealing with astronomical time scales, as seen in the example of converting the age of the universe into seconds. The process involves several steps of converting from larger to smaller units, making sure at each step to use the correct number of days in a year, hours in a day, minutes in an hour, and seconds in a minute.

To tackle time conversions, start with the largest time unit and work down to the smallest unit, ensuring that each previous unit cancels out to leave only the desired unit. The use of scientific notation is also crucial when dealing with very large numbers that result from such conversions.

• Always verify the time unit conversion chain for accuracy.
• Use scientific notation for large numbers to simplify calculations and improve readability.

Converting between volume units is a task often encountered, for instance, when adapting a recipe or comparing fuel efficiency in different countries. A fundamental conversion is from cubic meters to liters, foundational in many scientific and engineering calculations.

In the provided solution, volume is converted from cubic meters to liters, taking advantage of the direct conversion factor where 1 cubic meter equals 1000 liters. By multiplying the volume value by this factor, the conversion is easily achieved. This kind of unit conversion is common in fields like fluid dynamics and chemistry.

• Identify volume units in metric and imperial systems: liters, cubic meters, gallons, etc.
• Use the appropriate conversion factor to transform between units.

Scientific notation is a concise way to express very large or very small numbers, often used in time and volume conversions involving unwieldy numbers. It comprises a number between 1 and 10 multiplied by a power of 10.

For example, when converting the age of the universe into seconds, the result is a vast number best expressed in scientific notation to improve clarity and avoid errors in calculation. This notation is universally recognized in science and engineering and facilitates easier arithmetic operations on large numbers.

• Learn to recognize and use scientific notation for large-scale calculations.
• Scientific notation standardizes measurements and enhances communication among scientists and students.