Earth's population is about 7.2 billion. Suppose that every...

Earth's population is about 7.2 billion. Suppose that every person on Earth participates in a process of counting identical particles at the rate of two particles per second. How many years would it take to count $6.0 \times 10^{23}$ particles? Assume that there are 365 days in a year.

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Key Concepts

Scientific Notation

Scientific notation is a method of expressing very large or very small numbers in the form a × 10^n, where a is a number between 1 and 10 and n is an integer. This representation simplifies calculations and comparisons by consolidating the magnitude into a power of ten, which is especially useful in fields like physics and chemistry when dealing with quantities such as Avogadro’s number.

Aggregate Rate Computation

Aggregate rate computation involves determining a total rate when multiple sources or agents contribute simultaneously. In problems of this type, the individual rates are multiplied by the number of contributors to find the overall process rate, allowing for the estimation of how long it takes to complete a task when numerous efforts are combined.

Unit Conversion

Unit conversion is the process of converting measurements from one unit to another using conversion factors. In time-related problems, this typically involves converting seconds to minutes, minutes to hours, hours to days, and days to years. Proper unit conversion is essential for ensuring that the computed time is accurately represented in the desired units.

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