Use the prefix multipliers to express each measurement without exponents. c. 7.4 * 103 g

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Identify the prefix multiplier that corresponds to the exponent in the measurement. In this case, 10^3 corresponds to the prefix 'kilo' (k).

Rewrite the measurement using the identified prefix. Replace 10^3 with 'kilo' to express the measurement in terms of kilograms.

The original measurement is 7.4 * 10^3 g. Using the prefix 'kilo', rewrite this as 7.4 kg.

Ensure that the units are consistent and correctly represent the original measurement without exponents.

Verify that the conversion is correct by checking that 1 kilogram equals 10^3 grams.

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주요 개념

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Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically formatted as a product of a number between 1 and 10 and a power of ten. For example, 7.4 * 10^3 g means 7.4 multiplied by 1000, which equals 7400 g.

Metric Prefixes

Metric prefixes are used to denote specific powers of ten in the metric system, allowing for easier communication of measurements. Common prefixes include 'kilo-' for 10^3, 'mega-' for 10^6, and 'milli-' for 10^-3. In the case of 7.4 * 10^3 g, the prefix 'kilo-' can be used to express the measurement as 7.4 kg.

Unit Conversion

Unit conversion involves changing a measurement from one unit to another while maintaining the same quantity. This process often requires the use of conversion factors, which are ratios that express how many of one unit are equivalent to another. In this context, converting grams to kilograms involves dividing by 1000, thus 7400 g becomes 7.4 kg.