Use the prefix multipliers to express each measurement without exponents. a. 1.2×10⁻⁹ m

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Identify the prefix that corresponds to the exponent in the measurement. In this case, the exponent is -9.

Recall that the prefix for 10^{-9} is 'nano', which is abbreviated as 'n'.

Rewrite the measurement using the prefix 'nano' instead of the exponent. Therefore, 1.2 \(\times\) 10^{-9} m becomes 1.2 nanometers.

Ensure that the unit is correctly expressed with the prefix, resulting in 1.2 nm.

Double-check the conversion to confirm that the prefix accurately represents the original exponent.

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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 involves writing a number as a product of a coefficient (between 1 and 10) and a power of ten. For example, 1.2 * 10^-9 m indicates that the number is 1.2 multiplied by 0.000000001, which is a very small measurement.

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 'nano-' (10^-9), 'micro-' (10^-6), and 'milli-' (10^-3). In the case of 1.2 * 10^-9 m, the appropriate prefix is 'nanometers,' which simplifies the expression to 1.2 nm.

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another, often involving the use of conversion factors. In this context, converting from scientific notation to a metric prefix requires understanding the relationship between the units and applying the correct prefix to express the measurement in a more manageable form.

Use the prefix multipliers to express each measurement without exponents. a. 1.2×10−9 m