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Chapter 8: Problem 37

Convert the units of mass. $$409 \mathrm{cg}= ______ g$$

Short Answer

Expert verified
4.09 grams

Step by step solution

01

Understand the Conversion Factor

Recognize that 1 centigram (cg) is equal to 0.01 grams (g). This is the conversion factor that will be used.
02

Set Up the Conversion Equation

Write the equation to convert centigrams to grams: \( 409 \text{ cg} \times \frac{1 \text{ g}}{100 \text{ cg}} \) This equation uses the fact that 1 g = 100 cg.
03

Perform the Multiplication

Multiply 409 by the conversion factor: \( 409 \times 0.01 = 4.09 \) This results in 4.09 grams.

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Key Concepts

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

Mass Conversion
Mass conversion involves changing a value of mass from one unit to another. This is common in science and daily activities. In this exercise, we need to convert centigrams (cg) to grams (g). Having the ability to convert units allows for easy comparison and better understanding of quantities.

  • When converting units, it's essential to know the relationship between the units you're converting. For example, knowing how many grams are in a centigram.
  • Conversions are often done using conversion factors, a multiplier that equates two different units. This process ensures that the quantity's value does not change, only the unit description.
  • Practicing mass conversions with both large and small numbers is helpful, as it builds familiarity with different units and their relationships.
Centigrams to Grams
To convert centigrams to grams, we use the conversion factor that relates the two units directly. One centigram (cg) is equal to 0.01 grams (g). This means that for every 100 centigrams, you get 1 gram. This conversion factor is key in transforming the units.

In the example given:
  • You start with 409 centigrams (cg).
  • Then, you apply the conversion factor: 1 cg = 0.01 g.
  • Set up the equation to find the number of grams: \[ 409 \text{ cg} \times \frac{1 \text{ g}}{100 \text{ cg}} = 4.09 \text{ g} \]
  • Finally, perform the multiplication: 409 \times 0.01 = 4.09 grams.
This step-by-step process makes sure you apply the conversion correctly, leading to an accurate result.
Conversion Factor
A conversion factor is a number used to change one set of units to another by multiplying or dividing. It is crucial in unit conversions because it ensures the quantity remains the same, only the unit changes.

Here鈥檚 a simple way to understand conversion factors:
  • In this exercise, the conversion factor is derived from the relationship between centigrams and grams. Specifically, 1 cg = 0.01 g.
  • This means the conversion factor is 0.01. Every centigram is 0.01 grams.
  • When you multiply 409 cg by the conversion factor (0.01), you shift to the gram unit:
\[ 409 \text{ cg} \times 0.01 = 4.09 \text{ g} \]

  • This removal of the old unit (cg) and introduction of the new unit (g) happens seamlessly due to the conversion factor.
  • By understanding and using the right conversion factor, you facilitate accurate and hassle-free conversions between units.

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