Question

A minivan sells for 33,200 dollars. Give the price of the minivan in (a) kilodollars and (b) megadollars.

Short answer

The minivan costs 33.2 kilodollars or 0.0332 megadollars.

Step-by-step solution

Define the Units

First, understand what 'kilodollars' and 'megadollars' mean. One kilodollar (k$) is equivalent to 1,000 dollars (1 k$ = 1,000 $), and one megadollar (M$) is equivalent to 1,000,000 dollars (1 M$ = 1,000,000 $).

Convert Dollars to Kilodollars

To convert 33,200 dollars to kilodollars, divide the dollar amount by 1,000 since 1 kilodollar equals 1,000 dollars.\[33,200 \text{ dollars} \div 1,000 = 33.2 \text{ kilodollars}\]

Convert Dollars to Megadollars

Next, convert 33,200 dollars to megadollars by dividing the dollar amount by 1,000,000 because 1 megadollar equals 1,000,000 dollars.\[33,200 \text{ dollars} \div 1,000,000 = 0.0332 \text{ megadollars}\]

Key concepts

Understanding Kilodollars

When we talk about kilodollars, it's a way to express large sums in a simpler form that is easier to comprehend and work with. The prefix 'kilo-' in the metric system means one thousand. Therefore, 1 kilodollar (often abbreviated as k\() is

• equivalent to 1,000 dollars
• used for sums in the thousands to simplify the expression

For example, if a car costs 5,000 dollars, you can say it costs 5 kilodollars. This is handy for both budgeting and financial discussions, where you frequently encounter large numbers. In this particular exercise, to convert 33,200 dollars into kilodollars, you simply divide by 1,000. The conversion looks like this: \[33,200 \text{ dollars} \div 1,000 = 33.2 \text{ kilodollars}\]So, instead of \)33,200, the expression simplifies to 33.2 k$.

Exploring Megadollars

Just like kilodollars, megadollars are a useful unit for discussing even larger sums of money. The prefix 'mega-' stands for one million. Hence, 1 megadollar (usually written as M\() equals 1,000,000 dollars. This unit is particularly helpful in contexts like national budgets or large commercial transactions.

• Makes it easier to communicate multi-million-dollar figures
• Reduces the number of digits and potential for errors

With our minivan cost of 33,200 dollars, converting it into megadollars requires dividing by 1,000,000. Follow this operation:\[33,200 \text{ dollars} \div 1,000,000 = 0.0332 \text{ megadollars}\]This conversion signifies that the minivan's cost is 0.0332 M\), offering a less cluttered way to express substantial amounts of money.

Understanding Mathematical Conversion

Mathematical conversion is all about translating one set of units to another while maintaining the correct numerical relationship. It involves:

• Identifying the conversion factor (the relationship between the two units)
• Applying this factor to the original number

In our exercise, you start by identifying the conversion factors:

• 1 kilodollar = 1,000 dollars
• 1 megadollar = 1,000,000 dollars

The steps involve dividing the dollar amount by these factors to change the units from dollars into kilodollars or megadollars. For instance, converting dollars into kilodollars is straightforward:\[\text{Amount in kilodollars} = \frac{\text{Amount in dollars}}{1,000}\]In contrast, converting to megadollars requires a bit more shrinking of the number, given it is a larger unit of measure:\[\text{Amount in megadollars} = \frac{\text{Amount in dollars}}{1,000,000}\]This process illustrates the ease and power of conversion, making it possible to express and understand various scales of monetary figures.