Math Mammoth Exponents and Scientific Notation

57 pages
(includes answers)

Sample pages (PDF)
Contents
Laws of Exponents, Part 1
Scientific Notation: Small Numbers
Scientific Notation in Calculations

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Math Mammoth Exponents and Scientific Notation is a worktext with explanations and exercises about the basic exponent laws and scientific notation, meant for 8th grade math.

We start out with a review of the concept of an exponent and of the order of operations. The next lesson first reviews multiplication of integers, and then focuses on powers with negative bases, such as (−5)³.

Then we get to the “meat” of the book: the various laws of exponents. The first lesson on that topic allows students to explore and to find for themselves the product law and the quotient law of exponents. After that, students find out the logical way to define negative and zero exponent by looking at patterns. They practice simplifying various expressions with exponents, both with numerical values and with variables.

The lesson “More on Negative Exponents” focuses on expressions with a negative exponent in the numerator, such as 7/(a⁻⁴). This is to prepare students for calculations that ask them to find how many times bigger one number is than another, when the numbers are written in scientific notation.

Next, students practice applying the power of a power law:  (aⁿ)^m = a^nm in the lesson ”Laws of Exponents, Part 2“.

Then the book has one more lesson on the laws of exponents (“Laws of Exponents, Part 3”), which summarizes the laws and gives more practice. It is presented here to give a summary and to give practice on all exponent laws, including the power of a quotient law which was not dealt with a lot in the previous lessons.

Then we turn our attention to scientific notation, first learning how it is used with large numbers and then with small numbers. The lesson on significant digits follows, helping students to know how to round final answers in calculations with measurements.

The last topic of the book is calculations with numbers given in scientific notations. These calculations, naturally, involve many scientific topics such as the atomic world or astronomy.

The book ends with a review lesson. The answers are appended.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.