Problem 23 - Intermediate Algebra

Question

In 2010 , the United States alone accounted for \(20.2 \%\) of the world's total energy consumption, using 103.3 quadrillion British thermal units (Btu). What was the world's energy consumption in \(2010 ?\) Round to the nearest quadrillion. ce: U.S. Energy Information Administration)

Step-by-Step Solution

Answer

The world's energy consumption in 2010 was approximately 511 quadrillion Btu.

Step 1: Understanding the Percentage

The problem states that the United States used 103.3 quadrillion Btu, which accounted for 20.2% of the world's total energy consumption. This means that 103.3 quadrillion Btu is 20.2% of the total world consumption.

Step 2: Setting Up the Equation

To find the total world energy consumption, we set up the equation based on the percentage: \[ 0.202 imes \text{World Consumption} = 103.3 \text{ quadrillion Btu} \]Here, 0.202 is the decimal form of 20.2%.

Step 3: Solving for World Consumption

To find the total world consumption, divide both sides of the equation by 0.202:\[ \text{World Consumption} = \frac{103.3}{0.202} \]Now, perform the division to find the value.

Step 4: Calculating the Total

Calculating the division:\[ \text{World Consumption} = \frac{103.3}{0.202} \approx 511.39 \text{ quadrillion Btu} \]Rounding 511.39 to the nearest quadrillion gives 511 quadrillion Btu.

Key Concepts

Understanding Percentage Problems

When dealing with percentage problems, it's important to understand how percentages function. A percentage represents a fraction of 100 and simplifies the process of determining proportions of a whole. In practice, you commonly deal with percentages to express how one amount relates to another on a scale from 0 to 100.
If you're told that something is 20.2% of another value, like in our energy consumption example, this means you're looking at 20.2 parts out of every 100 parts of the total.

• To convert a percentage into its decimal form, divide the percentage by 100. For instance, 20.2% can be written as 0.202 in decimal.
• When solving for a whole using a given percentage, set up an equation where you know one part of the whole and the percentage it represents.

Referencing percentage problems is common in everyday tasks, such as calculating sales tax or determining discounts at a store. Recognizing how to manipulate these figures in different scenarios aids in making informed decisions or calculations.

Exploring World Energy Consumption

World energy consumption is a critical indicator of how resources are utilized globally. It reflects not only the demand for energy in various sectors but also the environmental impact of energy production and consumption. In 2010, the data shows significant consumption figures, with the United States consuming a large chunk of the world's energy.
Understanding energy consumption figures aids policymakers, researchers, and businesses in understanding trends and making decisions about energy policy.

• The total energy consumption of a country or region indicates the overall demand and reliance on energy sources, which can include fossil fuels, electricity, and renewable resources.
• Tracking these figures over time helps in assessing the sustainability of energy practices and the progress towards reducing carbon emissions.

It is important to interpret such data in the context of global initiatives to combat climate change and strive for more sustainable energy solutions.

Simplifying with Mathematical Division

Mathematical division is a fundamental operation, essential for calculating percentages and many other mathematical problems. In the realm of percentage calculations, division helps to isolate unknown variables, such as total world consumption in this exercise.
Here is a simple breakdown of how division plays a role:

• Given an equation where a part is equated to a percentage of the whole, dividing both sides by this percentage isolates the whole. This step is crucial, as in our energy calculation example, where solving for the total required dividing the known part by the percentage in decimal form.
• Performing the division accurately is key; rounding results correctly to reflect realistic outputs. For instance, energy consumption figures are often rounded to facilitate easier handling and better comprehension.

This operation underpins a variety of practical applications beyond just percentage problems, serving as a cornerstone for fields ranging from finance to engineering.