Problem 60 - Beginning and Intermediate Algebra

Question

It is estimated that \(\$ 37,800,000,000\) will be spent on information technology security systems in 2013 (Source:\(\mathrm{IDC})\)

Step-by-Step Solution

Answer

The estimated amount spent on information technology security systems in 2013 can be represented as \(37.8 \times 10^9\) dollars. To make it more readable, we can convert it into billions, which gives us \(37.8~\mathrm{billion}\) dollars.

Step 1: Understanding the Number Representation

We are given the number \(37,800,000,000\). To better understand the number, let's break it down into smaller units. The number can also be expressed as \(37.8 \times 10^9\) dollars.

Step 2: Converting to Billions

To make the number more readable, let's convert it into billions. Using the conversion of 1 billion = \(10^9\), we have: \(37.8 \times 10^9 = 37.8~\mathrm{billion}\) dollars. So, the estimated amount spent on information technology security systems in 2013 is \(37.8~\mathrm{billion}\) dollars.

Key Concepts

Number Representation

In mathematics and science, numbers can often get quite large, making them more challenging to manage. Representing these large numbers efficiently is crucial. This is where scientific notation comes in handy. In scientific notation, a number is expressed as a product of a number between 1 and 10 and a power of 10.
For example, the large number \(37,800,000,000\) can be expressed in scientific notation as \(37.8 \times 10^9\). This format is useful because it simplifies calculations and allows for easier comprehension of magnitude. When you look at \(10^9\), it tells us how many times to multiply 10 by itself, in this case, nine times, which equals to 1,000,000,000. The scientific notation thus breaks down the process to an understandable form using exponents.
It is essential to recognize how this notation helps in saving space and improving readability, especially as numbers grow in size across different fields such as economics or cosmology.

Billion Conversion

Converting numbers to different units requires understanding what those units represent. The concept of a "billion" can vary depending on where you are in the world, but today's common standard in the U.S. and many other countries is that 1 billion equals \(10^9\) or 1,000,000,000.
This conversion becomes practical when dealing with large sums of money or any quantitative data. For instance, the exercise mentions \(37,800,000,000\) dollars. By converting, we simplify it to \(37.8\) billion dollars, maintaining the same value but in a form that's easier to communicate and understand.
Remember, always align with the conversion standard used in your location or context, especially in academic or international settings. It ensures clarity and avoids misunderstandings in numerical data interpretation.

Information Technology Expenditure

Spending on information technology (IT) is a critical area in today's digital world. As technology continues to advance, so does the need for improved security systems. In 2013, it was projected that \(37,800,000,000\) dollars would be spent on IT security systems.

• **Importance of IT Expenditure**: With the rise of cyber threats, investing in IT security is not a luxury but a necessity. Organizations allocate significant budgets to safeguard data and maintain trust.
• **Growth Over Time**: Over the past decades, the expenditure on IT has been steadily increasing. This reflects the escalating importance of technology in all business operations and daily life.
• **Economic Impact**: High-spending in this sector influences economies by creating jobs, fostering innovation, and enhancing competitiveness in global markets.

Understanding this context helps appreciate why seemingly enormous numbers like \(37.8\) billion dollars are devoted to technology, highlighting the critical role IT expenditure plays in the modern economy.