Understanding Unit Conversion: Inches to Centimeters

Unit conversion is the process of changing a quantity from one unit of measurement to another unit of measurement of the same kind. In this question, we need to convert a length given in inches (a British or Imperial unit) into centimeters (an SI unit).

The Relationship Between Inches and Centimeters

The inch is a unit of linear length, widely used in countries like the United States. The centimeter is a unit of length in the International System of Units (SI), commonly used globally.

There is a standard, internationally agreed-upon conversion factor between inches and centimeters. This factor allows us to convert any length measured in inches into its equivalent length in centimeters, and vice versa.

Performing the Inch to Centimeter Conversion

The exact relationship between an inch and a centimeter is defined as:

\( 1 \text{ inch} = 2.54 \text{ centimeters} \)

To convert a value given in inches to centimeters, you multiply the number of inches by this conversion factor, 2.54.

Step-by-Step Conversion of 1 Inch

We are asked to convert one inch into centimeters. Using the conversion factor:

• Start with the quantity in inches: 1 inch
• Use the conversion factor: \( \frac{2.54 \text{ cm}}{1 \text{ inch}} \)
• Multiply the quantity by the conversion factor to cancel out the 'inch' unit and be left with 'cm':
• \( 1 \text{ inch} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} \)
• Performing the multiplication: \( 1 \times 2.54 \text{ cm} = 2.54 \text{ cm} \)

Therefore, when you convert one inch from British to SI unit (centimeter), it becomes 2.54 cm.

Comparing Options

Let's look at the given options:

• Option 1: 25.4 cm (This would be 10 inches, as \( 10 \times 2.54 = 25.4 \))
• Option 2: 12 cm (There is no direct conversion factor involving 12)
• Option 3: 0.254 cm (This is one-tenth of an inch, not one inch)
• Option 4: 2.54 cm (This matches our calculated value)

Based on the standard conversion factor, 1 inch is equal to 2.54 cm.

Revision Table: Common Length Conversions

Additional Information on Unit Systems

Understanding different unit systems is crucial in various fields, including science, engineering, and trade.

• British/Imperial System: Historically based on customary units. Common units include inch, foot, yard, mile, ounce, pound, gallon. Used primarily in the United States.
• SI System (International System of Units): The modern form of the metric system. Based on base units like meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (thermodynamic temperature), mole (amount of substance), and candela (luminous intensity). Used by most countries worldwide for science, trade, and everyday measurements.
• Conversion factors like 1 inch = 2.54 cm provide the bridge between these systems, ensuring accurate communication and calculation across different regions and disciplines.