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Ch.1 - Introduction: Matter, Energy, and Measurement
All textbooksBrown 15th EditionCh.1 - Introduction: Matter, Energy, and MeasurementProblem 34c
Chapter 1, Problem 34c

Use appropriate metric prefixes to write the following measurements without use of exponents: c. 6.48×10-7 L

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Identify the appropriate metric prefix for the given exponent. In this case, the exponent is -7, which corresponds to the prefix 'nano' (n), where 1 nL = 10^{-9} L.
Convert the given measurement from liters to nanoliters. Since 1 nL = 10^{-9} L, you need to express 6.48 \times 10^{-7} L in terms of nanoliters.
To convert, divide the exponent of the given measurement by the exponent of the prefix. Here, you have 10^{-7} L and you want to convert to 10^{-9} L, so you divide -7 by -9.
Calculate the conversion factor: 10^{-7} L = 10^{2} nL, because -7 - (-9) = 2.
Multiply the original measurement by the conversion factor: 6.48 \times 10^{2} nL.

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Key Concepts

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

Metric Prefixes

Metric prefixes are standardized terms used to denote specific powers of ten in the metric system. They simplify the representation of large or small quantities by providing a shorthand way to express these values. For example, 'nano-' represents 10^-9, while 'micro-' represents 10^-6, allowing for easier communication of measurements in scientific contexts.
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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, as it condenses them into a more manageable form. In the case of 6.48×10^-7 L, the coefficient is 6.48, and the exponent indicates the decimal point's position, which can be converted to a metric prefix.
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Conversion to Standard Form

Converting a measurement from scientific notation to standard form involves rewriting the number without exponents. This process requires understanding how to shift the decimal point based on the exponent's value. For example, 6.48×10^-7 L becomes 0.000000648 L, which can also be expressed using the appropriate metric prefix, '648 nL' (nanoliters), for clarity and conciseness.
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