Lengths

In mathematics, length is a measurement of the extent of something along its greatest dimension. Length is typically measured in units such as meters, centimeters, inches, feet, and so on. Understanding lengths is important in various mathematical and practical contexts, including geometry, physics, engineering, and everyday measurements.

Units of Length

There are several common units of length used in different contexts:

• Meter (m): The standard unit of length in the metric system. One meter is equal to 100 centimeters or 1000 millimeters.
• Centimeter (cm): One hundredth of a meter. Commonly used for smaller measurements.
• Kilometer (km): Equal to 1000 meters. Used for longer distances, such as in travel or geography.
• Inch (in): A unit of length in the imperial and US customary systems, equal to 1/12 of a foot.
• Foot (ft): Equal to 12 inches. Commonly used for measuring height and distance in the United States and other countries.
• Yard (yd): Equal to 3 feet. Often used for measuring longer distances, such as in sports or construction.

Converting Between Units

It's important to be able to convert between different units of length. Here are some common conversion factors:

• 1 meter = 100 centimeters
• 1 meter = 1000 millimeters
• 1 kilometer = 1000 meters
• 1 inch = 2.54 centimeters
• 1 foot = 12 inches
• 1 yard = 3 feet

Measuring Lengths

When measuring lengths, it's important to use the appropriate unit and instrument. For example, a ruler or tape measure is typically used for smaller lengths, while larger distances may be measured with a measuring wheel or GPS device.

Practice Problems

Here are some practice problems to test your understanding of lengths:

1. Convert 2.5 meters to centimeters.
2. If a notebook is 8.5 inches long, what is its length in centimeters?
3. A marathon is 26.2 miles long. What is the length of the marathon in kilometers?
4. How many millimeters are there in 2.3 meters?

For each problem, remember to use the appropriate conversion factor and unit.

Summary

Understanding lengths and being able to work with different units of length is an important skill in mathematics and everyday life. Practice converting between units and measuring various lengths to reinforce your understanding.