Question

Inches are used in the United States, but centimeters are used by scientists and in the rest of the world. Look at a ruler that is marked in both inches and centimeters. a. Make a graph of centimeters versus inches so that the y-axis is centimeters and the x-axis is inches. b. Convert 12 in. to centimeters. c. How many inches is 10 cm? d. How many inches is 1 cm?

Short answer

a. Plot: y = 2.54x. b. 12 in = 30.48 cm. c. 10 cm = 3.937 in. d. 1 cm = 0.3937 in.

Step-by-step solution

Understanding the Conversion

We need to know that 1 inch equals 2.54 centimeters. This conversion factor will help us create a relationship between inches and centimeters that we can use for conversion.

Drawing the Graph

On the graph, label the x-axis as inches and the y-axis as centimeters. When plotting, remember that each inch corresponds to 2.54 centimeters, so for x values (inches) 1, 2, 3, ..., n, the y values (centimeters) will be 2.54, 5.08, 7.62, ..., 2.54n respectively. This line will have a constant slope.

Convert 12 inches to Centimeters

Using the conversion factor, multiply 12 inches by 2.54: \( 12 \times 2.54 = 30.48 \) cm.

Convert 10 Centimeters to Inches

To find out how many inches 10 cm is, we reverse the conversion: divide 10 cm by 2.54: \( 10 \div 2.54 \approx 3.937 \) inches.

Find Inches in 1 cm

Using the conversion factor backward, for 1 cm, divide 1 by 2.54: \( 1 \div 2.54 \approx 0.3937 \) inches.

Key concepts

Centimeters to Inches

The process of converting centimeters to inches is straightforward, once you understand the conversion factor involved. The key factor to remember here is that 1 inch equals 2.54 centimeters. This means if you want to convert from a smaller metric unit, centimeters, to a larger one, inches, you have to divide by 2.54.
Calculating this is simple:

• Take the measurement in centimeters.
• Divide that number by 2.54.

So, for example, if you have 10 cm and want to know how many inches that is, you perform this calculation: \[ 10 \div 2.54 \approx 3.937 \] This tells us that 10 centimeters is approximately 3.937 inches.

Inches to Centimeters

Converting inches to centimeters is a common task, especially when dealing with international measurements, as the metric system is used globally. Luckily, thanks to the simple relation that 1 inch equals 2.54 centimeters, this conversion is pretty straightforward.
Here’s how you can convert inches to centimeters:

• Take the measurement in inches.
• Multiply that measurement by 2.54 to convert it to centimeters.

As a practical example, if you have a measurement of 12 inches, converting it to centimeters involves this calculation:\[ 12 \times 2.54 = 30.48 \] Thus, 12 inches is equal to 30.48 centimeters.

Metric System

The metric system is a universal method of measurement based on the meter, kilogram, and second. It is used widely around the world, making it essential for scientific, industrial, and international applications.
One of the greatest advantages of the metric system is its simplicity. Measurements are based on powers of ten, making conversions between units straightforward. Here are some key features:

• Base units like the meter, liter, and gram.
• Consistent scaling with prefixes like kilo (1000) and centi (1/100).
• Used in almost all countries, except a few, making it globally accepted.

This standardized system allows for uniformity and precision when exchanging information internationally.

Measurement Conversion

Measurement conversion is vital when navigating between different systems of measurement, such as the metric system and the imperial units used in the United States. Understanding conversion processes allows one to move between systems easily.
Key points for successful measurement conversion:

• Know the conversion factor; for instance, 1 inch equals 2.54 centimeters.
• Use multiplication or division depending on the unit conversion direction.
• Being familiar with unit scales and their applications can greatly enhance measurement accuracy.

With these, you can confidently convert units, make precise calculations, and understand measurements in various contexts, bridging the gap between different measurement systems.