Problem 28 - Introductory Chemistry Atoms First

Question

Express the distance \(24,000,000,000 \mathrm{~m} \pm 100\) million \(\mathrm{m}\) using the appropriate Greek prefix.

Step-by-Step Solution

Answer

The given distance can be expressed as \(24\ \mathrm{G}\mathrm{m} \pm 0.1\ \mathrm{G}\mathrm{m}\) using the appropriate Greek prefix (Giga).

Step 1: Identify the Appropriate Greek Prefix

For expressing large distances, Greek prefixes can make the numbers more manageable. The standard Greek prefixes used for distances are: - Kilo (k): \(1,000\ \mathrm{m}\) - Mega (M): \(1,000,000\ \mathrm{m}\) - Giga (G): \(1,000,000,000\ \mathrm{m}\) - Tera (T): \(1,000,000,000,000\ \mathrm{m}\) In this case, the given distance is \(24,000,000,000\ \mathrm{m}\), which can be written as \(24 \times 1,000,000,000\ \mathrm{m}\). Since the value is in billions, we will use the prefix Giga (G).

Step 2: Convert the Distance to Giga Meters

Now that we have identified the appropriate Greek prefix (Giga), we can rewrite the distance in Giga meters. We know that \(1\ \mathrm{G}\mathrm{m} = 1,000,000,000\ \mathrm{m}\). So, we can write: Distance = \(24,000,000,000\ \mathrm{m}\ \pm 100\ \mathrm{million}\ \mathrm{m}\) Dividing both the values by \(1,000,000,000\), we get: Distance = \(24\ \mathrm{G}\mathrm{m} \pm 0.1\ \mathrm{G}\mathrm{m}\) So, the given distance can be expressed as \(24\ \mathrm{G}\mathrm{m} \pm 0.1\ \mathrm{G}\mathrm{m}\) using the appropriate Greek prefix.

Key Concepts

Greek prefixes

In the world of measurements, Greek prefixes serve as a useful tool to easily handle large numbers. They help us express very large or very small quantities in a more convenient and readable way. For instance, imagine you need to write down a distance of one billion meters. It would certainly be cumbersome to write all those zeros! Instead, Greek prefixes like "Giga" make our job much easier.

Here's a quick guide on some common Greek prefixes used for meter measurements:

• Kilometer (k): Equal to 1,000 meters.
• Megameter (M): Equal to 1,000,000 meters.
• Gigameter (G): Equal to 1,000,000,000 meters.
• Terameter (T): Equal to 1,000,000,000,000 meters.

Using these prefixes not only saves space but also makes it easier to read and comprehend large figures swiftly. Next time you see a large number, try converting it using Greek prefixes!

Gigameters

A Gigameter is not a term you hear every day, but it stands as one of the Greek prefixes employed in communicating vast distances. In essence, a Gigameter (Gm) represents one billion meters. It's particularly useful in fields like astronomy, where celestial bodies are distantly located.

For example, the distance from Earth to the Sun is approximately 150 million kilometers or 150,000 Gm. This makes it much easier and manageable to convey such vast spans without writing long sequences of numbers.

Using the Gigameter isn't limited to professional astronomers. Anyone needing to express large measurements in a simplified manner can utilize this prefix effectively. So if you ever find the need to include a large distance in your homework or project, the Gigameter might just be your best friend!

Measurement conversion

Measurement conversion might sound a bit overwhelming at first, but it is a handy tool once you get the hang of it. It is all about changing one unit of measure into another. In our exercise, we see measurement conversion in practice when converting meters into Gigameters.

Let's break it down:

• First, identify the correct prefix or unit needed for conversion. In our case, it was "Giga" which corresponds to a factor of 1,000,000,000.
• Second, take the given measurement, say 24,000,000,000 meters, and divide it by the conversion factor to get the new measurement in the desired unit.

So, dividing 24,000,000,000 meters by 1,000,000,000, you'll find that it equals 24 Gigameters (Gm).

Measurement conversion allows us to easily scale down or scale up our measurements, making them much simpler to work with. Just remember, being familiar with conversion factors and Greek prefixes opens up a world of easier computation and understanding.