Question

Find the speed of light in feet per nanosecond, to three significant figures.

Short answer

Answer: The speed of light in feet per nanosecond, rounded to three significant figures, is approximately 0.984 feet per nanosecond.

Step-by-step solution

Identify the speed of light in meters per second

The speed of light in vacuum, denoted by the symbol 'c', is approximately 299,792,458 meters per second. This is the value we will use to convert to feet per nanosecond.

Convert meters to feet

In order to convert meters to feet, we need to use the conversion factor: 1 meter = 3.28084 feet. So, to convert the speed of light from meters per second to feet per second, we can multiply by this conversion factor: c (feet/second) = c (meters/second) × 3.28084 (feet/meter) This gives us c (feet/second) ≈ 983,571,056 feet per second.

Convert seconds to nanoseconds

Now, we need to convert the time unit from seconds to nanoseconds. There are 1,000,000,000 (10^9) nanoseconds in a second. To convert the speed of light from feet per second to feet per nanosecond, we can divide by this conversion factor: c (feet/nanosecond) = c (feet/second) ÷ 10^9 (nanoseconds/second) This gives us c (feet/nanosecond) ≈ 0.983571056 feet per nanosecond.

Round to three significant figures

Finally, we want to express the answer to three significant figures. Rounding 0.983571056 feet per nanosecond to three significant figures gives us approximately 0.984 feet per nanosecond. So, the speed of light in feet per nanosecond, to three significant figures, is approximately 0.984 feet per nanosecond.

Key concepts

Unit Conversion

Unit conversion is a fundamental tool in physics and engineering, allowing us to translate measurements from one set of units to another. This process is essential because different countries and fields may use different units for measuring the same physical quantity.

To perform a unit conversion, we typically use a conversion factor, which is a ratio that expresses the equivalence between two different units. For example, 1 meter is equivalent to approximately 3.28084 feet. To convert a measurement given in meters to feet, you would multiply the measurement by this conversion factor.

In converting the speed of light from meters per second to feet per second, we utilised the conversion factor, multiplying the speed of light by 3.28084 (since 1 meter = 3.28084 feet). Such conversions often require adjusting scales from larger to smaller units or vice versa, such as converting seconds to nanoseconds, which involves division by a factor of 1,000,000,000.

Physical Constants

Physical constants are fixed, unchanging numbers that describe the fundamental properties of the universe. In physics, constants like the speed of light ('c'), gravitational constant ('G'), and Planck's constant ('h') are used to predict the behavior of objects and waves under various conditions.

The speed of light in a vacuum, approximately 299,792,458 meters per second, is one of these constants. Recognized worldwide, it is denoted by the symbol 'c' and features prominently in Albert Einstein's theory of relativity. A fundamental constant like this is critical when we need precise and standardized values for scientific calculations, ensuring everyone uses the same baseline. When undergoing unit conversion for these constants, maintaining their integrity and precision is crucial for accurate scientific communication and reproduction of results.

Significant Figures

Significant figures play a pivotal role in ensuring the precision of measurements. They are the digits in a number that carry meaning contributing to its measurement resolution. It includes all non-zero numbers, any zeros between them, and any trailing zeros in the decimal portion.

When converting units or using physical constants, it's essential to consider significant figures to convey the appropriate level of precision. For instance, in our exercise, after converting the speed of light into feet per nanosecond, we express the answer to three significant figures. This means we only keep three digits that give meaningful information about the precision of our calculation, which in this case are 0.984 feet per nanosecond. This approach aids us in avoiding the overstatement of precision where the trailing digits beyond the third do not carry significant weight in the measured value's accuracy.