Question

A new movie earns \(\$ 114,000,000\) in its opening weekend. Express this amount in (a) gigadollars and (b) teradollars.

Short answer

114 million dollars equals 0.114 gigadollars and 0.000114 teradollars.

Step-by-step solution

Understand Prefixes

The prefixes 'giga' and 'tera' are part of the metric system. 'Giga' means one billion, which is \(10^9\), and 'tera' means one trillion, which is \(10^{12}\). Our task is to convert the movie earnings \(\$114,000,000\) into these units.

Convert Dollars to Gigadollars

To convert dollars to gigadollars, we divide by \(10^9\), since one gigadollar is one billion dollars. So, our conversion is: \[\frac{114,000,000}{10^9}=0.114\, \text{gigadollars}.\]

Convert Dollars to Teradollars

To convert dollars to teradollars, divide by \(10^{12}\), since one teradollar is one trillion dollars. The calculation is: \[\frac{114,000,000}{10^{12}}=0.000114\, \text{teradollars}.\]

Key concepts

Unit Conversion

Unit conversion is a useful skill that allows us to express measurements using different units. By understanding how to convert between units, we can easily compare quantities and understand their scale in practical contexts, like finances.
In the context of money, converting large sums into units like gigadollars or teradollars gives us a broader perspective on scale.

• To perform a conversion, you need the equivalence factor between units.
• This factor indicates how many of one unit makes up another.

For example, to convert dollars to gigadollars or teradollars, you divide by the respective equivalence factors ( 10^9 for gigadollars and 10^{12} for teradollars). To convert a value:

• Identify the conversion factor needed.
• Divide the original value by this conversion factor.
• The result is your converted value.

This ability to convert units can simplify complex problems and help in visualizing large-scale numbers.

Gigadollars

Let's dive into gigadollars. Gigadollars are a way to express billions of dollars. It derives from the metric prefix 'giga,' which means one billion, or 10^9.
This form of measurement is helpful when dealing with numbers in the billions, as it condenses large figures into more manageable terms.
With this measurement:

• We simplify big figures, aiding comprehension and communication.
• Calculating with gigadollars often involves dividing numbers in dollars by a billion.

For example, if a movie earned 114,000,000 dollars during its opening weekend, its equivalent in gigadollars would be 0.114 gigadollars. This is calculated by dividing 114,000,000 by 10^9. It makes understanding and expressing large financial values more straightforward.

Teradollars

Teradollars allow us to explore the realm of trillions of dollars. The term 'tera' originates from the metric prefix that signifies one trillion or 10^{12}. It becomes quite practical when dealing with vast financial figures.
Transforming dollars into teradollars involves dividing by one trillion. This conversion is especially useful when working with national budgets or large-scale economic projects. Some benefits of using teradollars include:

• Clarity in discussing expansive financial data.
• Efficiency in calculations, as massive numbers are simplified.

For instance, our movie's earnings of 114,000,000 dollars equate to 0.000114 teradollars when divided by 10^{12}. Understanding this conversion helps in grasping the true scale of colossal sums.