1.) (2 pts.) Using long division, write the fraction \( 5 / 27 \) as a decimal.

To convert the fraction \( 5 / 27 \) into a decimal using long division, you divide 5 by 27. First, since 5 is less than 27, you start with 0 and add a decimal point, bringing the 5 down to 50. Now, 27 goes into 50 one time (1), which gives you 27. Subtracting that from 50 leaves you with 23. Bring down another 0 to get 230. Next, 27 goes into 230 eight times (8), which gives you 216. Subtracting that from 230 leaves you with 14. Bring down another 0 to get 140. Then, 27 goes into 140 five times (5), giving you 135. Subtracting that leaves you with 5. The process repeats at this stage, so you get \( 0.185185... \). Therefore, \( 5 / 27 \approx 0.185 \) recurring. The final result, as a decimal, is \( 0.\overline{185} \). Did you know that the decimal \( 0.185 \) is not just fascinating on paper? It pops up unexpectedly in real-life scenarios, especially in probability and finance! For instance, if you consider the chances of certain outcomes when rolling dice or calculating the odds of winning a game, equivalents like \( 5 / 27 \) help quantify those scenarios. Additionally, if you're performing long division, remember that placing your decimal correctly is essential! A common mistake is forgetting to bring down the zeros properly, leading to cutoff decimals. Always keep track of the digits you’re working with! Plan ahead by aligning your numbers neatly to avoid the confusion.