Question

Convert the following to the equivalent indicated. \(350 \mathrm{~mm}=\) _______ \(\mathrm{in}\)

Short answer

350 mm is approximately 13.78 inches.

Step-by-step solution

Understand the unit conversion

We need to convert millimeters (mm) to inches (in). The conversion factor between millimeters to inches is that 1 inch equals 25.4 millimeters.

Set up the conversion factor

We use the conversion factor to set up our equation. We know that: \[ 1 \text{ in} = 25.4 \text{ mm} \] Thus, to convert millimeters to inches, we will divide the number of millimeters by 25.4.

Perform the division

Using the conversion factor, we have: \[ 350 \text{ mm} = \frac{350}{25.4} \text{ inches} \] Now, calculate the division: \[ = 13.7795 \text{ inches} \]

Round the result

To finalize our conversion, we can round the result to a convenient precision. Typically, inches are rounded to two decimal places. Thus, 13.7795 inches rounds to 13.78 inches.

Key concepts

Millimeters to Inches

Converting from millimeters to inches is a common task, especially in contexts where precise measurements are necessary, such as in engineering or design. Understanding this conversion involves knowing that millimeters are a smaller unit of length compared to inches.
Millimeters are part of the metric system, while inches are used in the imperial system. Typically, converting between these units is essential when dealing with international projects that might involve both systems.
To convert millimeters to inches, it's important first to grasp that this operation requires division due to the larger size of an inch compared to a millimeter. Hence, you divide the number of millimeters by a specific conversion factor to successfully switch to inches.

Conversion Factor

The conversion factor is a crucial piece of knowledge for converting lengths from millimeters to inches. It acts as a bridge between the metric and imperial systems. The standardized conversion factor for this specific conversion is that 1 inch equals 25.4 millimeters.
Understanding this factor makes the task straightforward:

• This means if you have a measure in millimeters, dividing it by 25.4 will give you the length in inches.
• This conversion factor is reliable and widely used, ensuring consistent results across different measurements.

Setting up the proper equation using this factor is key. Taking 350 millimeters as an example: \[ 350 \text{ mm} \times \frac{1 \text{ in}}{25.4 \text{ mm}} \]This simplifies to dividing 350 by 25.4, giving a result in inches.

Rounding

Rounding is an essential step when dealing with measurements, ensuring that the final answer is both practical and understandable. After converting millimeters to inches using the division step, you will often end up with a long decimal number.
To make this result more usable, particularly when precision to many decimal places isn't necessary, you round the number to a suitable precision. For lengths measured in inches, it's common to round the number to two decimal places.

• This precision suffices for most practical applications like construction, crafts, or even academic work.
• In our example, the result after the division was 13.7795 inches.

Therefore, rounding this value to two decimal places gives you 13.78 inches, which is concise and sufficient for many practical purposes.