About how many centimeters are in 6.25 inches if 1 inch is about 2.5 centimeters? Show your reasoning.
The Correct Answer and Explanation is:
To convert inches to centimeters, you multiply the number of inches by the conversion factor of 2.5 centimeters per inch. Given that ( 1 \text{ inch} = 2.5 \text{ cm} ), the calculation for ( 6.25 ) inches is as follows:
[
6.25 \, \text{inches} \times 2.5 \, \text{cm/inch} = 15.625 \, \text{cm}.
]
So, ( 6.25 \, \text{inches} ) is approximately ( 15.625 \, \text{cm} ).
Explanation
- Understanding the Problem:
The goal is to convert a length measurement from inches to centimeters. Since 1 inch equals approximately 2.5 centimeters, this problem involves straightforward multiplication. - Using the Conversion Factor:
The conversion factor tells us how many centimeters are in one inch. Multiplying the number of inches by this factor scales the length appropriately. For every inch, we add ( 2.5 \, \text{cm} ). - Setting up the Calculation:
The given length is ( 6.25 \, \text{inches} ). Multiply ( 6.25 ) by ( 2.5 ) to convert:
[
6.25 \times 2.5 = 15.625.
]
This means ( 6.25 \, \text{inches} ) corresponds to ( 15.625 \, \text{cm} ). - Double-Checking the Work:
Breaking down the multiplication step-by-step:
- ( 6 \times 2.5 = 15.0 )
- ( 0.25 \times 2.5 = 0.625 )
- Adding these together: ( 15.0 + 0.625 = 15.625 ).
- Answer Presentation:
Always include the correct units to ensure clarity. The answer is ( 15.625 \, \text{cm} ).
This process demonstrates the use of unit conversion and the importance of clear steps to arrive at the precise answer. For practical purposes, the value might be rounded depending on the context. If rounded to two decimal places, the result is ( 15.63 \, \text{cm} ).