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When we look at the stock market, a common measure of performance is the change in stock price over a period of time. To determine whether a stock's value has appreciated or depreciated, investors compare the current price to a past price. In the exercise, we are asked to compare the price of a stock from Coca-Cola Company over a five-year span, from 2003 to 2008. The price in 2003 was \(39, and by 2008 it had increased to \)56.

This change reflects the stock's growth, and to make sense of how significant this change is, it's essential to express it as a percentage. This allows for a standardized comparison with other stocks or investments, regardless of their price ranges. By calculating the percent increase, we can communicate the change in a clear, concise manner that is easily interpretable and comparable for investors, analysts, or students studying finance.

The concept of percentage calculation is fundamental in various fields including finance, statistics, and everyday life. In financial contexts, specifically, we often express changes as percentages because they provide a relative sense of the size of the change.

Using the percent increase formula \( \frac{{\text{{New Value}} - \text{{Old Value}}}}{{\text{{Old Value}}}} \times 100\% \) lets us find out how much something has increased relative to its original value. In the given exercise, we applied this formula to find the increase of the Coca-Cola Company stock price from 2003 to 2008. By plugging in the stock prices for those years into the formula, we calculated a percent increase that reflects the relative change in value over time.

It's important to understand each step: subtracting to find the change, dividing by the original value to find the proportional change, and then multiplying by 100 to convert this proportion into a percentage. This process converts a stock price change into a meaningful percentage that can be used to make informed decisions.

Rounding decimals is a mathematical process used to make numbers easier to work with or to express them more meaningfully. When dealing with percentages, it's common to round to a certain number of decimal places, often to the nearest whole number or to the nearest tenth.

In our stock price increase example, after calculating we arrived at 43.59%. For practicality and simplicity, we round this value. The exercise specifies to round to the nearest tenth of a percent, which means looking at the hundredths place (the second decimal place) and rounding the tenth's place up or down accordingly. Since the hundredths place is a 9, we round up, changing our value to 43.6%.

Rounding makes statistical or financial data cleaner and it's crucial for clear communication in reports and presentations. While exact numbers can provide precise information, rounded figures often suffice for a summary or comparison, and they are generally easier for people to read and comprehend. However, it's essential to round only at the final step to maintain the accuracy of the calculation throughout the process.