Problem 24 - Prealgebra

Question

Make the following conversions in the metric system by multiplying by the appropriate conversion factor. Write your answers as whole numbers or decimals. \(67 \mathrm{mm}\) to centimeters

Step-by-Step Solution

Answer

67 mm is equal to 6.7 cm.

Step 1: Understanding the Units

The problem requires us to convert from millimeters (mm) to centimeters (cm). In the metric system, both these units measure length.

Step 2: Establishing the Conversion Factor

Since 1 centimeter is equal to 10 millimeters, the conversion factor from millimeters to centimeters is \( \frac{1}{10} \).

Step 3: Applying the Conversion Factor

To convert millimeters to centimeters, we multiply the number of millimeters by the conversion factor. This means: \[ 67 \text{ mm} \times \frac{1}{10} = 6.7 \text{ cm} \].

Step 4: Final Result

After performing the multiplication, we find that 67 millimeters equals 6.7 centimeters.

Key Concepts

Understanding Length Measurement

Length measurement is a fundamental concept used to quantify the size of objects, the distance between them, or the dimensions of spaces. In the metric system, which is commonly used worldwide, length is typically measured in units like millimeters (mm), centimeters (cm), meters (m), and kilometers (km). These units are part of a decimal-based system, making conversions straightforward.

In the metric system, each unit is a power of ten smaller or larger than the others, which helps in easy calculations. Understanding how units relate to one another is the key to mastering metric conversions. When dealing with problems related to measuring length activities, keep in mind that:

• Millimeters are very small units, mainly used for precise measurements.
• Centimeters are commonly used in everyday applications, like measuring small objects or height.
• Meters and kilometers are used for larger distances and dimensions.

The Role of a Conversion Factor

The conversion factor is crucial in converting units within the metric system. It is a number used to change the units of a measurement, without affecting its actual value.

For example, converting from millimeters to centimeters involves using a specific conversion factor. When you know that 1 centimeter equals 10 millimeters, you can establish that the conversion factor from millimeters to centimeters is \( \frac{1}{10} \). This means you multiply the amount in millimeters by this factor to find the equivalent in centimeters.

Using conversion factors simplifies calculations because:

• They standardize the process of conversion.
• They offer a quick reference, making calculations faster.
• They ensure accuracy, as they rely on a systematic approach to unit relations.

Steps in Millimeter to Centimeter Conversion

Converting from millimeters to centimeters is a common task and can be easily performed by understanding the relationship between these two units. Here's a simple approach to transforming millimeters into centimeters:

Start by identifying the number of millimeters you have. For example, if you have 67 millimeters, that's the value you'll work with. Then, apply the conversion factor. Since we know from our earlier discussion that 1 centimeter is equal to 10 millimeters, use the conversion factor \( \frac{1}{10} \).

Multiply the millimeter value by this conversion factor:
\[ 67 \text{ mm} \times \frac{1}{10} = 6.7 \text{ cm} \]

This multiplication gives us the answer directly and shows that 67 millimeters equals 6.7 centimeters. Practicing this ensures that converting between these units becomes second nature, easing your journey in mastering metric conversions.