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

Use appropriate metric prefixes to write the following measurements without use of exponents: g. 5.1×102 cm

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1
Identify the metric prefix that corresponds to the exponent given in the problem. In this case, 10^2 corresponds to the prefix 'hecto-', which is used for 100.
Rewrite the measurement using the identified metric prefix. Since 5.1 × 10^2 cm is equivalent to 5.1 hecto-centimeters, you can express it as 5.1 hectocentimeters.
Alternatively, convert the measurement to a more commonly used metric unit if needed. For example, since 1 meter is 100 centimeters, you can convert 5.1 × 10^2 cm to meters by dividing by 100.
Perform the conversion by dividing 5.1 × 10^2 cm by 100 to express the measurement in meters.
Write the final measurement in meters without using exponents, ensuring clarity and precision in the expression.

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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, 'centi-' represents one-hundredth (10^-2), so 5.1×10^2 cm can be expressed as 5.1 m when converted to meters.
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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. In the given measurement, 5.1×10^2 cm indicates that the value is 5.1 multiplied by 100, which equals 510 cm, and can be converted to a more manageable metric prefix.
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Unit Conversion

Unit conversion involves changing a measurement from one unit to another while maintaining the same quantity. In this case, converting centimeters to meters requires knowing the relationship between these units, specifically that 1 m equals 100 cm. Thus, to convert 510 cm to meters, you divide by 100, resulting in 5.1 m.
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Related Practice
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Use appropriate metric prefixes to write the following measurements without use of exponents: c. 6.48×10-7 L

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Use appropriate metric prefixes to write the following measurements without use of exponents: d. 1.81×10-2 s

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Make the following conversions: a. 72 °F to °C

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Make the following conversions: c. 233 °C to K

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Make the following conversions: d. 315 K to °F