Problem 111 - Prealgebra

Question

The Pentagon has spent $100 million over a six-month period responding to and repairing damage from cyber-attacks and other computer network problems. What’s the average amount of money spent per month over that time? Round your answer to the nearest hundredth of a million. Associated Press-Times-Standard 4/19/09

Step-by-Step Solution

Answer

Average spent per month is 16.67 million.

Step 1: Understanding the Total Amount

The problem states that the Pentagon has spent a total of $100 million over a six-month period. This amount is given as the total expenditure for that duration.

Step 2: Understanding the Period

The time period mentioned in the problem is six months. This is the duration over which the total expenditure is spread.

Step 3: Calculating the Average Monthly Expenditure

To find the average monthly expenditure, divide the total amount spent ($100 million) by the number of months (6). This will give the average amount spent per month. \[\text{Average per month} = \frac{100\, \text{million}}{6} = 16.67\, \text{million}\]

Step 4: Rounding to the Nearest Hundredth of a Million

The result of the division is approximately 16.66666... million. To round this to the nearest hundredth, look at the thousandths place: 16.67 million.

Key Concepts

Division

Division is an important mathematical operation used to distribute a number into equal parts. In this case, it helps us find how much money was spent each month.
To calculate the average amount spent, we divided the total expenditure of \(100 million by the six months during which it was spent. This division tells us the monthly expenditure. Mathematically, we express this as:

• Total amount spent: \)100 million
• Number of months: 6
• Average per month = \( \frac{100 \text{ million}}{6} \)

This division results in approximately 16.66666... million dollars per month. By dividing, you determine the equal monthly distribution of the total amount. This concept is frequently used in budgeting and financial planning.

Rounding Numbers

Rounding is a technique used to simplify numbers, making them easier to work with or understand. It involves adjusting the number to its nearest significant place value, which is very helpful in many real-world applications like financial statements.
In our exercise, the result of the division was 16.66666... million. You can round this number to make it simpler to read and use. We round to the nearest hundredth (second decimal place) by looking at the third decimal place:

• If the digit in the third decimal place is 5 or more, we round up the second decimal place.
• If it is less than 5, we round down.

In this case:

• Original number: 16.66666...
• Third decimal digit: 6
• Result after rounding: 16.67 million

Rounding gives a clearer representation of the monthly expenditure and simplifies further calculations or comparisons.

Understanding Periods

Periods refer to the intervals of time over which events or expenditures occur. In our exercise, understanding the period is crucial to calculate the average monthly expenditure. The period given was six months over which a total of $100 million was spent.
Understanding periods helps break down total expenditure over time to see how funds are allocated evenly. With a six-month period:

• The amount spent is distributed uniformly across these months.
• Helps assess if the expenditure was consistent or varied over time.

Recognizing the time duration of an event or activity is essential in financial planning and analysis. It simplifies determining averages and observing trends over specific periods, leading to informed decision-making.