Problem 45
Question
The International Association for Wireless Communication predicted annual wireless data revenues in 2011 of \(\$ 55.4\) billion, compared to \(\$ 280.8\) million in 1996 . Find the increase in revenues, writing the answer in place value notation. (Source: www.ctia.org, Oct. 11, 2011)
Step-by-Step Solution
Verified Answer
The increase is \( 55,119,200,000 \) dollars.
1Step 1 - Identify the Given Values
Identify the annual wireless data revenues for the years provided. In 1996, the revenue was \(280.8\) million dollars. In 2011, the revenue was \(55.4\) billion dollars.
2Step 2 - Convert Values to the Same Units
Convert both values to the same unit for easier comparison. There are 1,000 million dollars in a billion dollars. Therefore, \(55.4\) billion dollars is equivalent to \(55.4 \times 1000 = 55,400\) million dollars.
3Step 3 - Calculate the Increase in Revenue
Subtract the revenue in 1996 from the revenue in 2011. \(55,400 \text{ million} - 280.8 \text{ million} = 55,119.2 \text{ million}\).
4Step 4 - Express the Answer in Place Value Notation
Write the final answer in proper place value notation: \( 55,119.2 \text{ million} \text{ dollars } = 55,119,200,000 \text{ dollars} \).
Key Concepts
Unit ConversionSubtractionPlace Value NotationBillion to Million Conversion
Unit Conversion
Unit conversion is essential when comparing two quantities that are initially in different units. In this exercise, we need to compare revenues given in billions and millions. To do this effectively, it's helpful to convert them to the same unit.
In general, remember that:
So, converting 55.4 billion dollars into millions, we perform the multiplication: 55.4 billion × 1,000 = 55,400 million. Now, both values are on the same scale, making it easier to compare and subtract.
In general, remember that:
- 1 billion = 1,000 million
So, converting 55.4 billion dollars into millions, we perform the multiplication: 55.4 billion × 1,000 = 55,400 million. Now, both values are on the same scale, making it easier to compare and subtract.
Subtraction
Subtraction is straightforward when both numbers are in the same unit. To find out how much the revenue has increased, you subtract the old value from the new one.
Here, with the revenues both converted to millions, the steps are:
Performing the subtraction gives us:
55,400 million - 280.8 million = 55,119.2 million.
This means the revenue increased by 55,119.2 million.
Here, with the revenues both converted to millions, the steps are:
- New Revenue: 55,400 million
- Old Revenue: 280.8 million
- Increase: 55,400 million - 280.8 million
Performing the subtraction gives us:
55,400 million - 280.8 million = 55,119.2 million.
This means the revenue increased by 55,119.2 million.
Place Value Notation
Place value notation helps us write large numbers clearly and accurately. It involves grouping digits into sets of three, starting from the right.
For the number 55,119.2 million, imagine it's like this:
The fully written-out version of 55,119.2 million in dollars is:
55,119,200,000 dollars.
Place value notation ensures clarity and precision, making it easier to read and understand large numbers.
For the number 55,119.2 million, imagine it's like this:
- 5 | 5 | 1 | 1 | 9.2
The fully written-out version of 55,119.2 million in dollars is:
55,119,200,000 dollars.
Place value notation ensures clarity and precision, making it easier to read and understand large numbers.
Billion to Million Conversion
Converting billions to millions involves simple multiplication. Since 1 billion = 1,000 million, any number in billions can be converted by multiplying by 1,000.
For example:
This step is crucial to avoid errors and to make sure you're comparing like with like, as we did when calculating the revenue increase between 1996 and 2011.
For example:
- 55.4 billion = 55.4 × 1,000 = 55,400 million
This step is crucial to avoid errors and to make sure you're comparing like with like, as we did when calculating the revenue increase between 1996 and 2011.