Table of contents
- 0. Review of Algebra4h 16m
- 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 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Exponents
1:06 minutes
Problem 80c
Textbook Question
Textbook QuestionIn Exercises 77–86, write each number in scientific notation. 579,000,000,000,000,000
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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 very large or very small numbers in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 579,000,000,000,000,000 can be expressed as 5.79 x 10^17, where 5.79 is the coefficient and 17 is the exponent indicating the number of places the decimal point has moved.
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Exponent Rules
Exponent rules are mathematical guidelines that govern the operations involving powers of numbers. Key rules include the product of powers (a^m * a^n = a^(m+n)), the power of a power ( (a^m)^n = a^(m*n)), and the power of a product ( (ab)^n = a^n * b^n). Understanding these rules is essential for manipulating numbers in scientific notation effectively.
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Place Value
Place value refers to the value of a digit based on its position within a number. In the context of scientific notation, recognizing the place value helps in determining how many places the decimal point moves when converting a standard number to scientific notation. For instance, in 579,000,000,000,000,000, the placement of digits indicates that the decimal point moves 17 places to the left to form 5.79.
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