Understanding Exponents: Definition, Evaluation, and Powers of Ten
This lesson covers the fundamental concepts of exponents, including definitions of base and exponent, how to evaluate expressions with exponents, and the representation of numbers using powers of ten. Students will learn how to express multiples of ten as exponents, such as recognizing that 100 is 10 squared. Additionally, the lesson explains how to write numbers in expanded form using powers of ten. Practice problems and examples ensure a comprehensive understanding of these essential mathematical principles.
Understanding Exponents: Definition, Evaluation, and Powers of Ten
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Presentation Transcript
Exponents Lesson 2-8
Vocabulary exponent – the number of times a number is multiplied by itself. base – the number that is being multiplied. exponent 83 base This is read “8 to the 3rd power” or “8 cubed.” It means 8 x 8 x 8.
Evaluating Exponents 25 = 2 x 2 x 2 x 2 x 2 = 32 = 6 x 6 x 6 = 216 63 1.34 = 1.3 x 1.3 x 1.3 x 1.3 = 2.8561
Exponents with a base of 10 • Any multiple of ten can be expressed as an exponent with a base of ten. • The base is 10. The number of zeroes gives us the exponent. • Example: 100 = 102 • 10,000 = 104 1,000,000 = 106
Writing in Expanded Form Using Powers of 10 • First, write the problem in expanded form. • Then, change each term to a multiplication of the value and its place. • Change the place values to exponents with powers of 10.
7, 946 Example 7, 000 + 900 + 40 + 6 (7 x 1,000) + (9 x 100) + (4 x 10) + (6 x 1) 7 x 103 + 9 x 102 + 4 x 101 + 6
