Use prefix multipliers to express each measurement without exponents. a. 12.1 * 108 g

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Identify the given value and the unit: The given value is 12.1 × 10⁸ g. The goal is to rewrite this value using a prefix multiplier without exponents.

Recall the SI prefix multipliers and their corresponding powers of 10. For example, kilo (k) = 10³, mega (M) = 10⁶, giga (G) = 10⁹, etc.

Determine the appropriate prefix multiplier for the given exponent. Since the exponent is 10⁸, the closest prefix multiplier is mega (M), which corresponds to 10⁶.

Rewrite the value by factoring out 10⁶ from 10⁸. This means dividing 10⁸ by 10⁶, leaving 10². The value becomes 12.1 × 10² M (megagrams).

Simplify the expression further by multiplying 12.1 by 10² to eliminate the exponent. The final result will be expressed in megagrams (Mg) without exponents.

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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 involves writing a number as a product of a coefficient (between 1 and 10) and a power of ten. For example, 12.1 * 10^8 can be expressed as 1.21 * 10^9, which simplifies calculations and comparisons.

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- (10^3), mega- (10^6), and giga- (10^9). By converting a measurement into a form that uses these prefixes, one can express large quantities in a more manageable way, such as converting grams to kilograms.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. This is essential in chemistry for ensuring that measurements are in compatible units for calculations. For example, converting grams to kilograms involves dividing by 1000, which is crucial when using metric prefixes to express measurements without exponents.