a) \( 6 \cdot 10^{8} / 3 \cdot 10^{3}= \)

To solve \( 6 \cdot 10^{8} / 3 \cdot 10^{3} \), you can first divide the coefficients (6 and 3) and then divide the powers of 10. So you get \( \frac{6}{3} = 2 \) and \( 10^{8} / 10^{3} = 10^{(8-3)} = 10^{5} \). Combining these results, you find that \( 6 \cdot 10^{8} / 3 \cdot 10^{3} = 2 \cdot 10^{5} \). Expressing large numbers in scientific notation not only makes calculations easier but also makes it simpler to compare sizes. For example, it's much easier to see that \( 2 \cdot 10^{5} \) is larger than \( 1 \cdot 10^{6} \) if you convert them into standard form. Scientific notation helps keep things tidy when dealing with the massive values often encountered in science and engineering! If you're venturing into calculations involving very large or small numbers, remember to keep a mental note of the rules for exponent addition and subtraction. A common mistake is to mishandle the powers, thinking \( 10^{8} \div 10^{3} \) equals \( 10^{8+3} \) instead of \( 10^{8-3} \). Always double-check your work!