Decimals are a way of expressing numbers that are not whole. They are used to represent parts of a whole number. In a decimal, the digits to the right of the decimal point represent parts of one whole unit. The position of each digit to the right of the decimal point indicates its place value.

Each digit in a decimal has a specific place value, just like in whole numbers. The place values to the right of the decimal point are powers of 10, but they are negative powers. The place values to the right of the decimal point are tenths, hundredths, thousandths, and so on.

To read a decimal number, say the whole number part, then say "and", and read the digits to the right of the decimal point as if they were whole numbers. For example, the decimal 3.25 is read as "three and twenty-five hundredths". When writing decimals, the decimal point is placed between the whole number part and the fractional part.

To compare decimals, start from the left and compare the digits in each place value position. If the digits are the same, move to the next place value to the right. The decimal with the larger digit in the leftmost non-equal place value position is the greater number. To order decimals, compare and arrange them from least to greatest or greatest to least.

Decimals can be added, subtracted, multiplied, and divided just like whole numbers. When performing these operations, it's important to align the decimal points to ensure accuracy in the results. When multiplying and dividing, the number of decimal places in the result is equal to the total number of decimal places in the numbers being multiplied or divided.

Rounding decimals involves determining which multiple of 10, 100, 1000, etc., a decimal is closest to. The digit to the right of the desired place value is used to determine whether the number should be rounded up or down.

Decimals can be converted to fractions by using the place value of the last digit. For example, 0.8 is equivalent to 8/10, which can be simplified to 4/5. Decimals can also be converted to percentages by multiplying by 100, or by moving the decimal point two places to the right.

Here are some key points to remember when working with decimals:

- Understand the place value of each digit in a decimal.
- Be able to read and write decimal numbers accurately.
- Know how to compare and order decimals.
- Practice performing basic operations with decimals.
- Learn how to round decimals to a specified place value.
- Be familiar with converting decimals to fractions and percentages.

Remember to practice these skills through exercises and problem-solving to reinforce your understanding of decimals.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

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.