Carry out the following conversions: (a) 0.105 in. to mm

Verified step by step guidance

1. Start by identifying the conversion factors needed. We know that 1 inch is equal to 2.54 centimeters.
2. Convert inches to centimeters using the conversion factor: 0.105 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}}.
3. Now, convert centimeters to millimeters. Remember that 1 centimeter is equal to 10 millimeters.
4. Use the conversion factor to convert centimeters to millimeters: \text{result in cm} \times \frac{10 \text{ mm}}{1 \text{ cm}}.
5. Combine the steps to find the final conversion from inches to millimeters.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. This involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. For example, to convert inches to millimeters, one can use the conversion factor that 1 inch equals 25.4 millimeters.

Metric System

The metric system is an internationally recognized decimal system of measurement based on powers of ten. It includes units such as meters for length, grams for mass, and liters for volume. Understanding the metric system is essential for performing conversions, as it provides a standardized framework for measuring and comparing quantities.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another by multiplying by conversion factors. It ensures that the units cancel appropriately, leading to the desired unit in the final answer. This method is particularly useful in chemistry and physics for ensuring that equations are dimensionally consistent.