A decimal is a way of representing a part of a whole number. It is used to express numbers that are not whole. Decimals are based on powers of 10, and they are written to the right of the decimal point. The decimal point separates the whole number part from the fractional part.

In the decimal 25.75, the whole number part is 25 and the fractional part is .75. The decimal point separates the whole number and the fractional part.

Each digit in a decimal has a place value, based on its position to the right of the decimal point. The place values of decimal digits are powers of 10, but they are negative powers of 10. For example, in the decimal 25.75, the 5 is in the tenths place, and the 7 is in the hundredths place.

Decimals can be converted to fractions and vice versa. To convert a decimal to a fraction, you can use the place value of the decimal. For example, the decimal 0.75 can be written as 75/100, which simplifies to 3/4.

Decimals can be added, subtracted, multiplied, and divided just like whole numbers. When performing operations with decimals, it is important to align the decimal points and carry out the operation as usual.

Rounding decimals involves choosing a specific place value to round to. For example, to round the decimal 3.789 to the nearest tenth, you would look at the digit in the hundredth place. If it is 5 or greater, you round up; if it is less than 5, you round down.

- Understand the place value of decimal digits.
- Be able to convert decimals to fractions and vice versa.
- Practice performing operations with decimals, such as addition, subtraction, multiplication, and division.
- Learn how to round decimals to a specified place value.
- Review real-world applications of decimals, such as money and measurements.

Study GuideIntroduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer keyIntroduction to Percent

Number and Operations (NCTM)

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

Work flexibly with fractions, decimals, and percents to solve problems.

Develop meaning for percents greater than 100 and less than 1.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity

Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multi-step problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.

Connections to the Grade 7 Focal Points (NCTM)

Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.