Base in Mathematics

In mathematics, the term "base" refers to the number of different digits or combination of digits that a system of counting uses to represent numbers. The most common base used in everyday mathematics is base 10, also known as the decimal system, which uses the digits 0 through 9. However, other bases such as base 2 (binary), base 8 (octal), and base 16 (hexadecimal) are also used in computer science and digital electronics.

Base 10 (Decimal System)

The base 10 system uses 10 digits (0-9) to represent numbers. The place value of each digit in a number depends on its position within the number. For example, in the number 352, the digit 2 is in the ones place, the digit 5 is in the tens place, and the digit 3 is in the hundreds place.

Converting Between Bases

Converting numbers from one base to another involves understanding the place value system and the relationship between different bases. For example, to convert a number from base 10 to base 2 (binary), you can use the process of division and remainders. Conversely, to convert a binary number to decimal, you can use the process of expanding the number using powers of 2.

Study Guide for Bases

Understand the concept of place value and its importance in different number bases.
Practice converting numbers between different bases, such as base 10 to base 2, base 10 to base 8, and base 10 to base 16.
Learn the properties and uses of different number bases, particularly base 2 (binary) and base 16 (hexadecimal) in computer science and digital electronics.
Explore real-world applications of different number bases, such as binary code in computing and hexadecimal color codes in web design.
Master the skills of performing arithmetic operations (addition, subtraction, multiplication, and division) in different number bases.

◂Math Worksheets and Study Guides Sixth Grade. Area

The resources above cover the following skills:

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

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

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.