- Convert megawatts (MW) to watts (W) by multiplying by \(10^6\): \(9.102 \text{ MW} = \boxed{9.102 \times 10^6 \text{ W}}\).
- Convert milligrams (mg) to grams (g) by multiplying by \(10^{-3}\): \(193 \text{ mg} = \boxed{1.93 \times 10^{-1} \text{ g}}\).
- Convert microliters (\(\mu\)L) to liters (L) by multiplying by \(10^{-6}\): \(308 \mu\text{L} = \boxed{3.08 \times 10^{-4} \text{ L}}\).
- Convert meters (m) to centimeters (cm) by multiplying by \(10^2\): \(13.9 \text{ m} = \boxed{1.39 \times 10^3 \text{ cm}}\).
- Convert moles (mol) to millimoles (mmol) by multiplying by \(10^3\): \(1.68 \text{ mol} = \boxed{1.68 \times 10^3 \text{ mmol}}\).
Explanation
- Analysis and Methodology
The objective is to perform precise unit conversions for five distinct quantities, expressing each result in scientific notation while maintaining the appropriate number of significant figures as indicated by the original measurements. We will identify the necessary power-of-ten conversion factor for each SI unit prefix:
- Mega (M) represents a factor of \(10^6\).
- milli (m) represents a factor of \(10^{-3}\).
- micro (\(\mu\)) represents a factor of \(10^{-6}\).
- centi (c) represents a factor of \(10^{-2}\).
- mole (mol) to millimole (mmol) conversion involves a factor of \(10^3\).
Each conversion follows the principle of multiplying the original numerical value by the ratio of the new unit to the old unit, ensuring the significant digits of the source value are preserved.
- Conversion Calculations
- Convert 9.102 MW to W:
Since 1 MW = \(10^6\) W, we multiply 9.102 by \(10^6\).
\(9.102 \times 10^6 = 9.102 \times 10^6 \text{ W}\).
- Convert 193 mg to g:
Since 1 mg = \(10^{-3}\) g, we multiply 193 by \(10^{-3}\).
\(193 \times 10^{-3} = 0.193 \text{ g} = 1.93 \times 10^{-1} \text{ g}\).
- Convert 308 \(\mu\)L to L:
Since 1 \(\mu\)L = \(10^{-6}\) L, we multiply 308 by \(10^{-6}\).
\(308 \times 10^{-6} = 3.08 \times 10^{-4} \text{ L}\).
- Convert 13.9 m to cm:
Since 1 m = \(10^2\) cm, we multiply 13.9 by \(10^2\).
\(13.9 \times 10^2 = 1390 \text{ cm} = 1.39 \times 10^3 \text{ cm}\).
- Convert 1.68 mol to mmol:
Since 1 mol = \(10^3\) mmol, we multiply 1.68 by \(10^3\).
\(1.68 \times 10^3 \text{ mmol}\).
- Final Results
Based on the steps above, the completed conversions are:
- \(9.102 \text{ MW} = \boxed{9.102 \times 10^6 \text{ W}}\)
- \(193 \text{ mg} = \boxed{1.93 \times 10^{-1} \text{ g}}\)
- \(308 \mu\text{L} = \boxed{3.08 \times 10^{-4} \text{ L}}\)
- \(13.9 \text{ m} = \boxed{1.39 \times 10^3 \text{ cm}}\)
- \(1.68 \text{ mol} = \boxed{1.68 \times 10^3 \text{ mmol}}\)
Examples
Unit conversion is fundamental in scientific research and engineering. For instance, a chemist measuring substances in a laboratory must often convert between milliliters (mL) and liters (L) to calculate molar concentrations, or a biologist might convert micrometers (\(\mu\)m) to meters (m) when analyzing microscopic structures. Mastering these conversions, represented through scientific notation, ensures accuracy when scaling experiments from small laboratory benches to large-scale industrial production.