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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1:06 minutes

Problem 34

Textbook Question

Write each number in scientific notation. 3,590,000

Verified step by step guidance

Identify the significant figures in the number. For 3,590,000, the significant figures are 3, 5, and 9.

Place a decimal point after the first significant figure to form a number between 1 and 10. This gives us 3.59.

Count the number of places the decimal point has moved from its original position to the new position. In this case, it moves 6 places to the left.

Express the number as a product of the number formed in step 2 and 10 raised to the power of the number of places moved. This is written as 3.59 \times 10^6.

Combine the steps to write the original number in scientific notation: 3.59 \times 10^6.

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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 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 3,590,000 can be expressed as 3.59 x 10^6, where 3.59 is the coefficient and 6 is the exponent.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient are considered significant. For instance, in the number 3.59 x 10^6, the digits 3, 5, and 9 are significant, indicating the precision of the measurement.

Exponent Rules

Exponent rules govern how to manipulate powers of ten in mathematical expressions. When multiplying numbers in scientific notation, you add the exponents, while for division, you subtract them. Understanding these rules is essential for correctly performing operations with numbers expressed in scientific notation.