Question

The speed of light in a vacuum is approximately \(0.3 \mathrm{Gm} / \mathrm{s}\). What is the speed of light in meters per second?

Short answer

The speed of light is \(3 \times 10^8\) m/s.

Step-by-step solution

Understand the Given Units

The speed of light is given as 0.3 gigameters per second (Gm/s). A gigameter (Gm) is a unit of distance equal to one billion meters (1 Gm = 10^9 m). We need to convert the speed from gigameters per second to meters per second.

Set Up the Conversion

To convert gigameters to meters, recall that 1 Gm = 10^9 meters. Therefore, we multiply the given speed in Gm/s by this conversion factor to convert it to meters per second.

Perform the Conversion

The speed of light in meters per second is calculated by:\[0.3 imes 10^9 = 3 imes 10^8\]Thus, the speed of light in meters per second is \(3 imes 10^8\) m/s.

Verify the Result

Cross-check the calculation to ensure accuracy. Recalculating, \(0.3 imes 10^9\) indeed gives \(3 imes 10^8\). Therefore, the result is verified.

Key concepts

Unit Conversion

Unit conversion is a fundamental skill in science and math, allowing us to change measurements from one unit to another. It's like translating a language from one form to another to enhance understanding. Converting units often involves multiplying or dividing by a conversion factor. Here's a quick guide to unit conversions:

• Identify the units you have and the units you want.
• Find the conversion factor (e.g., 1 gigameter equals 1 billion meters).
• Multiply or divide by this factor to convert the measurement.

In the context of the speed of light, we started with gigameters per second and wanted meters per second.
Knowing that 1 Gm = 10^9 m, we multiplied by this factor to convert units, leading us to the familiar form for the speed of light.

Meters per Second

When discussing speed, meters per second (m/s) is a common unit used to measure velocity. It tells us how many meters an object travels in one second, making it straightforward to understand the concept of speed over time. The speed of light in a vacuum is often quoted in meters per second because:

• Meters are a standard unit of length in the metric system.
• Seconds are a universally used unit of time.
• Using these units simplifies calculations in physics and engineering.

The conversion of the speed of light from 0.3 Gm/s to 3 x 10^8 m/s illustrates how expressing speed in meters per second makes the information more accessible and practical for scientific applications.

Scientific Notation

Scientific notation is a method used to express very large or very small numbers in a compact form. It's especially useful in science where some numbers can be unwieldy.Here’s why scientific notation is valuable:

• It simplifies calculations involving big or tiny numbers by reducing errors.
• It provides a clear and concise way to represent magnitude.
• It's widely used in physics, chemistry, and engineering.

In the case of the speed of light, expressing 300,000,000 m/s as \(3 \times 10^8\) m/s makes it manageable.
This format helps with quick estimation and comparison between different measurements.
Understanding scientific notation is essential for interpreting and communicating scientific data effectively.