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Chapter 9: Problem 9

Convert the given unit of weight to the unit indicated. \(0.018 \mathrm{mg}\) to \(\mathrm{g}\)

Short Answer

Expert verified
The equivalent of \(0.018 \, \mathrm{mg}\) is \(0.000018 \, \mathrm{g}\)

Step by step solution

01

Define the Conversion Factor

Understand that there are 1000 milligrams in a gram. This is because the metric system is based on powers of 10, and each step up - milligrams to grams, grams to kilograms - multiplies by 1000.
02

Conversion

Divide the given value in milligrams (0.018 mg) by 1000. So it will be \(0.018 \, \mathrm{mg} / 1000 = 0.000018 \, \mathrm{g}\). This gives you the equivalent weight in grams.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Metric System
The metric system is an international system of measurement used almost universally. It is based on powers of ten, which makes it very simple to convert between units. This system is essential in science, medicine, and many other fields that require precise measurements. In this system, each unit鈥檚 name is prefixed to design its scale. For instance:
  • A milligram (mg) is one-thousandth of a gram.
  • A gram is the base unit for mass in the metric system.
This logical structure eliminates much of the complexity involved in converting units, as it often simply involves shifting decimal places. Understanding the metric system enables one to convert units by multiplying or dividing by factors of ten, making comparatively quick mental calculations possible.
Conversion Factor
A conversion factor is a number used to change one set of units to another, by multiplying or dividing. In the metric system, conversion factors are typically 10, 100, 1000, or higher powers of 10. For the original exercise, you are converting from milligrams to grams. Knowing that 1 gram equals 1000 milligrams gives you the conversion factor needed for this operation. When converting:
  • Divide when going from a smaller unit to a larger unit, as done in going from milligrams to grams.
  • Multiply when converting from a larger unit to a smaller unit, such as from grams to milligrams.
The conversion factor hence serves as a bridge between different measurement scales, ensuring that the quantities are accurately transformed without any change in their actual amount.
Mathematical Problem Solving
Mathematical problem solving when it comes to unit conversion is about applying the right mathematical operation to transform one unit into another seamlessly. The goal is to maintain accuracy and precision, ensuring the numerical value is correctly adjusted to reflect its new unit. In this exercise, simplicity is key:
  • Identify the given unit and the unit you need to convert to.
  • Apply the conversion factor that corresponds to these units, which in this case was determined by the metric system.
  • Divide or multiply as required to complete the conversion.
By clearly understanding the problem and breaking down the solution into manageable steps, solving these problems becomes straightforward. This method of breaking down a task is crucial in problem-solving across all areas of mathematics.

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