Question

An automobile airbag inflates in $35\mathrm{ms}$. What is the time of inflation in microseconds?

Short answer

35 ms inflates to 35,000 µs when converted.

Step-by-step solution

Understanding the Units

We are given the time of inflation in milliseconds (ms), and we need to convert it into microseconds (µs). Knowing the units and their conversion factors is key. We recognize that 1 millisecond equals 1,000 microseconds.

Setup the Conversion Factor

To convert milliseconds to microseconds, we use the conversion factor. Since 1 ms = 1,000 µs, we will multiply the given time in ms by this factor to get the time in µs.

Perform the Conversion

Given the time of inflation is 35 ms, we multiply by the conversion factor: $$35extmsimes1,000ext\mu s/ms=35,000ext\mu s$$

Conclusion Interpretation

The conversion process has shown that the automobile airbag inflates in 35,000 microseconds.

Key concepts

Understanding Time Conversion

Time conversion is a fundamental skill in the realm of mathematics and science. It involves changing a time measurement from one unit to another to make calculations or comparisons easier. For example, we may need to understand the time it takes for mechanical processes, like the inflation of an automobile airbag, in different units. The key to smooth conversion lies in grasping the equivalence of units. In this specific exercise, the goal is to convert milliseconds to microseconds. It's crucial to grasp that all time units are interrelated through multiples of 10, making conversion straightforward if we know the exact multiplication factor.

Converting Milliseconds to Microseconds

When we look at converting milliseconds (ms) to microseconds (µs), knowing the conversion factor is important. Specifically, 1 millisecond is equal to 1,000 microseconds. This relationship stems from the broader metric system, where time is often scaled by powers of ten. To convert any measurement from milliseconds to microseconds:

• Recognize that 1 ms equals 1,000 µs.
• Multiply the given number of milliseconds by 1,000 to obtain the equivalent in microseconds.

In our exercise, we have determined that 35 milliseconds can be converted easily to microseconds by multiplying with this precise conversion factor. This gives us 35,000 microseconds, showing how unit conversion can simplify and clarify understandings of different time frames.

Mastering Factor Multiplication

Factor multiplication is a straightforward method applied in unit conversions, helping us change measures from one unit to another. The factor becomes the bridge between different units. To successfully apply factor multiplication in this context:

• Identify the conversion factor necessary for your units, which is 1,000 for ms to µs.
• Apply this factor by multiplying it with your known measure—in our case, 35 ms.
• Compute the result to find your desired unit measurement. This requires basic multiplication and ensures your understanding of different scales of measurement.

By following this approach, we transform our measurement into the required unit. Factor multiplication reinforces numerical competency and helps you tackle complex problems by breaking them down into simple, manageable tasks.