Place value is the value of a digit depending on its position in a number. In our base-10 number system, each place value is ten times the value to its right. Understanding place value is essential for working with numbers and performing mathematical operations.

In a given number, each digit has a place value based on its position. The rightmost digit represents the ones place, the next digit to the left represents the tens place, the next one represents the hundreds place, and so on.

For example, in the number 3256:

- The digit 6 is in the ones place, with a value of 6.
- The digit 5 is in the tens place, with a value of 5 * 10 = 50.
- The digit 2 is in the hundreds place, with a value of 2 * 100 = 200.
- The digit 3 is in the thousands place, with a value of 3 * 1000 = 3000.

A place value chart is a helpful tool for understanding the value of each digit in a number. It organizes the number into its various place values, making it easier to comprehend the overall value of the number.

Thousands | Hundreds | Tens | Ones |
---|---|---|---|

3 | 2 | 5 | 6 |

Here are some key points to remember about place value:

- Each digit in a number has a place value based on its position.
- The place values are powers of 10, with the rightmost digit representing the ones place, the next representing the tens place, and so on.
- A place value chart can help visualize the value of each digit in a number.
- Understanding place value is crucial for performing addition, subtraction, multiplication, and division of multi-digit numbers.

Practice identifying place values in different numbers and using place value charts to represent numbers. This will help reinforce your understanding of place value and its importance in mathematics.

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.