Problem 11 - Elementary and Intermediate Algebra

Question

State which real number(s) correspond to each situation. Stock Market. The Dow Jones Industrial Average is an indicator of the stock market. On September 29 , \(2008,\) the Dow Jones fell a record 777.68 points. On October \(13,2008,\) the Dow Jones gained a record 936.42 points.

Step-by-Step Solution

Answer

The real numbers are \( -777.68 \) and \( 936.42 \).

Step 1: Identify the dates and changes

On September 29, 2008, the Dow Jones fell by 777.68 points. On October 13, 2008, the Dow Jones gained 936.42 points.

Step 2: Determine the corresponding real numbers

A fall in points is represented by a negative number, and a gain is represented by a positive number. Hence, a fall of 777.68 points on September 29 is denoted by \( -777.68 \). A gain of 936.42 points on October 13 is denoted by \( 936.42 \).

Key Concepts

negative numbers in stock market

In the stock market, changes in stock prices are often represented by real numbers. One important aspect is representing declines using negative numbers.
A negative number indicates a decrease. For example, if the Dow Jones Industrial Average (DJIA) fell by 777.68 points on a particular day, we represent this decline as \( -777.68 \).
This helps in quickly identifying losses. Understanding negative values is crucial for analyzing market performance. When you see a negative number, it signifies a reduction from a previous value.

positive numbers in stock market

Positive numbers, on the other hand, indicate an increase in stock prices. When the DJIA rises, we use positive numbers to represent the gain.
For instance, if the DJIA gained 936.42 points, this can be expressed as \( 936.42 \). Positive numbers show growth and improvement.
Recognizing positive changes helps in assessing market health. During times of growth, these numbers provide information on economic progress or recovery. Effective use of positive values is essential for investment decisions and predicting future trends.

real number representation

Real numbers play a significant role in the stock market as they offer precise and accurate representation of changes. The real numbers include both positive and negative values as well as zero.
They are used universally to indicate any gain or loss in stock points. For example, a 777.68 point fall in the DJIA is written as \( -777.68 \), while a 936.42 point rise is written as \( 936.42 \).
Using real numbers allows for better analysis and understanding of market trends. This comprehensive representation supports detailed financial scrutiny and aids in making informed decisions. By applying real numbers, we can represent very large or very small changes meticulously.