Question

Convert the following to the equivalent indicated. \(3 \mathrm{~cm}=\) _______ \(\mathrm{mm}\)

Short answer

3 cm is equivalent to 30 mm.

Step-by-step solution

Identify the Conversion Factor

First, we need to identify the conversion factor between centimeters and millimeters. In this case, 1 centimeter (cm) is equivalent to 10 millimeters (mm).

Set Up the Conversion

To convert from centimeters to millimeters, you multiply the number of centimeters by the conversion factor of 10. Thus, the formula to convert centimeters to millimeters is: \[ \text{millimeters} = \text{centimeters} \times 10 \]

Apply the Conversion

Now apply the conversion formula to the given measurement. Substitute the value given in the problem into the formula: \[ \text{millimeters} = 3 \times 10 \]

Calculate the Answer

Perform the multiplication to find the number of millimeters. \[ 3 \times 10 = 30 \]

Verify the Result

Ensure the result makes sense by reviewing the conversion factor and calculation steps. 3 cm multiplied by 10 gives us 30 mm, confirming our calculation is correct.

Key concepts

Understanding Conversion Factors

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. It's essential when converting measurements.
Conversion factors derive from the relationship between different units and come in the form of a simple ratio. They provide an easy path to switch from one unit to another without changing the quantity of the measurement.
In the context of centimeters to millimeters, the conversion factor is 10, meaning there are 10 millimeters in each centimeter.
To use a conversion factor:

• Identify the original and desired units.
• Find the conversion factor that relates these units.
• Multiply or divide by the conversion factor to convert the measurement.

This systematic approach ensures that the conversion is accurate. As both centimeters and millimeters are metric units of length, using the conversion factor of 10 is both straightforward and quick.

Converting Centimeters to Millimeters

Converting centimeters to millimeters is a simple process once you know the conversion factor.
Remember, for every 1 centimeter, there are 10 millimeters. This makes the conversion a multiplication task.
Take the number of centimeters you have, in this case, 3 cm, and multiply by the conversion factor 10 to convert to millimeters,

• The formula is: \ \[ \text{millimeters} = \text{centimeters} \times 10 \]
• For 3 cm: \ \[ \text{millimeters} = 3 \times 10 \]
• This gives you: \ \[ 30 \text{ mm} \]

This approach ensures you translate the measurement correctly, moving along the metric scale easily with simple multiplication.

Mathematical Calculation in Conversion

Performing mathematical calculations is at the core of unit conversions. It helps reaffirm understanding and accuracy.
In our example, we used multiplication since we moved from a larger unit (centimeter) to a smaller one (millimeter). Here, multiplication highlights how closely spaced the units are on the metric scale.
Steps for calculation include:

• Identify the original value and the conversion factor.
• Set up your equation, ensuring all units are correctly represented.
• Perform the multiplication. For instance, \ \[ 3 \times 10 = 30 \]

Review your calculations to ensure accuracy. This practice helps verify that the conversion factor was correctly applied and confirms the result.