Question

Students often have trouble relating measurements in the metric system to the English system they have grown up with. Give the approximate English system equivalents for each of the following metric system descriptions. I just purchased 12 meters of fabric at the sewing store for making new curtains.

Short answer

The 12 meters of fabric is approximately 39 feet and 4 inches in the English system.

Step-by-step solution

Convert meters to feet

To convert the given 12 meters of fabric to feet, we use the conversion factor 1 meter = 3.28084 feet. Multiply the number of meters (12) by the conversion factor: \(12 \text{ meters} * 3.28084 \frac{\text{feet}}{\text{meter}} = 39.37 \text{ feet}\) The 12 meters of fabric is approximately 39.37 feet.

Convert the decimal part of feet to inches

Now, let's find the inches equivalent of 0.37 feet. Since 1 foot = 12 inches, we can multiply the decimal part by 12: \(0.37 \text{ feet} * 12 \frac{\text{inches}}{\text{foot}} = 4.44 \text{ inches}\) The decimal part of the feet, 0.37 feet, is approximately 4.44 inches.

Combine feet and inches

Now, we have the equivalent measurements in both feet and inches. Combine the two values to obtain the final English system equivalent for 12 meters of fabric: \(39 \text{ feet} + 4.44 \text{ inches} \approx 39 \text{ feet } 4 \text{ inches}\) Hence, 12 meters of fabric is approximately 39 feet and 4 inches in the English system.

Key concepts

Measurement Conversion

Understanding measurement conversion is essential for comparing and applying different units of measure. When we talk about converting measurements, we're basically translating one unit into another to make sense of it in a different system or context. For instance, if you have traveled from Europe to the US, you might find the weather forecast given in Fahrenheit rather than Celsius, or the speed limits in miles per hour instead of kilometers per hour.
Measurement conversion requires knowledge of the relationship between the units, which is usually given by a conversion factor. Taking the exercise as an example, to convert from meters to feet, we use a specific conversion factor that tells us how many feet are in one meter.

Metric System

The metric system is an international standard for measurement, used by most countries around the world. It is a decimal-based system, meaning it’s organized in powers of ten, making it easier to understand and convert between units. The basic units include meters for length, liters for volume, and grams for mass. Larger and smaller quantities are expressed by adding prefixes like kilo-, centi-, or milli-.
The metric system is advantageous due to its simplicity and universal use in science and globally. In our exercise, the fabric length was initially given in meters, which is a metric unit of length. The importance of understanding the metric system lies in its widespread adoption and ease of scalability.

English System

The English system, also known as the Imperial system, is primarily used in the United States. It includes units like inches, feet, and pounds, and is not based on a decimal system, which can make conversions within this system more complex.
For example, 12 inches make a foot, and 3 feet make a yard. Unlike the metric system, where you would simply move a decimal point, converting within the English system often involves multiplication or division by numbers other than ten. This is why understanding conversions between the English system and the metric system, as shown in the exercise, is crucial for communication and comprehension in countries that use the English system.

Conversion Factors

Conversion factors are specific values that you can use to convert one unit of measurement into another. They are the key to changing quantities from one system of measurement to another, like from metric to English or vice versa.
In our textbook example, the conversion factors used are 1 meter equals 3.28084 feet and 1 foot equals 12 inches. By multiplying the original measurement by the appropriate conversion factor, you can translate the amount into the desired unit. It’s important to use accurate conversion factors to ensure the results are precise. In real life, this precision is crucial when following a recipe, sizing clothing, or working on construction projects.