Use prefix multipliers to express each measurement without exponents. a. 3.4x10^-16m

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Identify the appropriate prefix multiplier for the given exponent. In this case, the exponent is -16.

Recall that the prefix 'femto' (f) corresponds to 10^{-15}.

Since 10^{-16} is one order of magnitude smaller than 10^{-15}, we can express 3.4 \(\times\) 10^{-16} m as 0.34 \(\times\) 10^{-15} m.

Use the 'femto' prefix to rewrite the measurement: 0.34 femtometers (fm).

Ensure the final expression is clear and without exponents: 0.34 fm.

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Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a compact form, using powers of ten. It consists of a coefficient multiplied by 10 raised to an exponent, which indicates how many places to move the decimal point. For example, 3.4 x 10^-16 means 3.4 is multiplied by 0.00000000000000034, making it easier to read and work with extreme values.

Prefix Multipliers

Prefix multipliers are standard prefixes used in the metric system to simplify the representation of measurements. Each prefix corresponds to a power of ten, allowing for easier communication of quantities. For instance, 'femto-' represents 10^-15, so 3.4 x 10^-16 meters can be expressed as 0.034 femtometers (fm), making it more manageable to understand and use in calculations.

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 the appropriate prefix. This skill is essential in chemistry for ensuring that measurements are accurately represented and can be easily compared or calculated.

Use prefix multipliers to express each measurement without exponents. a. 3.4x10-16m