Problem 27 - 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. \(63.4 \mathrm{cm}\) to decimeters

Step-by-Step Solution

Answer

63.4 cm is 6.34 dm.

Step 1: Understand the Metric Conversion

To convert centimeters to decimeters, recognize the relationship between these units. In the metric system, 1 decimeter is equal to 10 centimeters.

Step 2: Set Up the Multiplication for Conversion

Use the conversion factor from Step 1. To convert centimeters to decimeters, divide the number of centimeters by 10 (the number of centimeters in one decimeter). The equation is: \[ \text{Decimeters} = \frac{\text{Centimeters}}{10} \]

Step 3: Perform the Calculation

Insert the given quantity of centimeters into the equation: \[ \text{Decimeters} = \frac{63.4}{10} \] This simplifies to \[ 6.34 \text{ decimeters} \].

Step 4: Write the Final Answer

Make sure the answer is presented in the requested format. The answer is 6.34, which can be written directly as a decimal.

Key Concepts

Decimeters

The metric system is an easy-to-use decimal-based measurement system. One of its units is the decimeter. A decimeter is a length measurement equivalent to one-tenth of a meter. This makes it larger than a centimeter but smaller than a meter. Understanding how larger metric units combine to form smaller ones is essential in the conversion process.

When considering larger measurements, using decimeters can simplify calculations or descriptions. For instance, something like the length of a tabletop can be conveniently expressed in decimeters for easier comprehension and fewer numbers compared to centimeters. This approach is particularly useful in practical, day-to-day applications and helps minimize errors in measurement.

Centimeters

Centimeters are another metric unit of length but are smaller than decimeters. One centimeter is defined as one-hundredth of a meter, making it ideal for measuring smaller objects like books or pencils. This smaller graduated size allows for more precision when measuring precisely.

In various real-world scenarios, centimeters are commonly used in sewing, construction, and many other fields where exact measurements are crucial. Understanding centimeter usage and their relationship to other metric units helps in performing accurate conversions and comparisons with ease.

Conversion Factor

A conversion factor is a number used to change units within the same measurement system, like from centimeters to decimeters. In metric conversions, recognizing these factors simplifies the transition between units.

The conversion factor for converting centimeters to decimeters is 10. This means you divide the number of centimeters by 10 to find the equivalent length in decimeters. Understanding this factor helps streamline conversions and minimize mistakes.

• Conversion factors always depend on the relationship between units.
• These relationships in the metric system are based on powers of ten, making it logical and straightforward.

By mastering conversion factors, students can become proficient in navigating various unit conversions easily and accurately.