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Ch.1 - Matter, Measurement & Problem Solving
Tro - Chemistry: A Molecular Approach 5th Edition
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371Not the one you use?Change textbook
All textbooksTro 5th EditionCh.1 - Matter, Measurement & Problem SolvingProblem 56a
Chapter 1, Problem 56a

Use prefix multipliers to express each measurement without exponents. a. 38.8×105 g c. 23.4×1011 m d. 87.9×10−7 L

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1
Identify the given measurement: 38.8 \(\times\) 10^5 \(\text{ g}\).
Recognize that the goal is to express this measurement using a prefix multiplier without exponents.
Recall the metric prefixes: kilo (10^3), mega (10^6), etc.
Determine which prefix multiplier is appropriate for 10^5. Since 10^5 is between 10^3 (kilo) and 10^6 (mega), we can express it in terms of kilograms (kg) by converting grams to kilograms.
Convert the measurement: 38.8 \(\times\) 10^5 \(\text{ g}\) = 38.8 \(\times\) 10^2 \(\text{ kg}\), which simplifies to 3880 \(\text{ kg}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Prefix Multipliers

Prefix multipliers are standard prefixes used in the metric system to denote specific powers of ten. For example, 'kilo-' represents 10^3, 'mega-' represents 10^6, and 'centi-' represents 10^-2. These prefixes simplify the expression of large or small quantities by allowing scientists to communicate measurements more efficiently without using exponents.
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Metric Prefixes Chart

Scientific Notation

Scientific notation is a method of expressing numbers as a product of a coefficient and a power of ten. It is particularly useful for handling very large or very small numbers. In the context of the question, the number 38.8 * 10^5 g can be converted into a more manageable form using prefix multipliers, which helps in understanding and comparing measurements easily.
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Standard Notation to Scientific Notation

Unit Conversion

Unit conversion involves changing a measurement from one unit to another while maintaining the same quantity. In this case, converting grams expressed in scientific notation to a more readable format using metric prefixes requires an understanding of how to translate between different units and their corresponding prefixes, ensuring clarity and accuracy in scientific communication.
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