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.

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.

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

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.

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

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

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

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.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.