Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:27 minutes

Problem 70

Textbook Question

In Exercises 65–76, write each number in decimal notation without the use of exponents. −8.17×10^6

Verified step by step guidance

Identify the given number in scientific notation: \(-8.17 \times 10^6\).

Understand that the exponent 6 indicates that the decimal point should be moved 6 places to the right.

Start with the number 8.17 and move the decimal point 6 places to the right.

Fill in any empty decimal places with zeros as you move the decimal point.

Write the final number in decimal notation without exponents.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically written as a product of a number between 1 and 10 and a power of ten. For example, the number 5,000 can be expressed as 5.0 × 10^3. Understanding this notation is essential for converting numbers into standard decimal form.

Decimal Notation

Decimal notation is the standard way of writing numbers using the base ten system, which includes digits from 0 to 9. It represents whole numbers and fractions using a decimal point. For instance, the number 2.5 in decimal notation indicates two whole units and five-tenths. Converting from scientific notation to decimal notation requires an understanding of how to manipulate the decimal point based on the exponent.

Negative Numbers

Negative numbers are values less than zero, represented with a minus sign (-). They are crucial in various mathematical contexts, including operations involving subtraction and in scientific notation where they can indicate a decrease in value. In the given example, the number -8.17 × 10^6 indicates a negative value, which must be accurately represented in decimal form as -8,170,000.