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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1:50 minutes

Problem 1

Textbook Question

In Exercises 1–14, write each number in decimal notation without the use of exponents.3.8X10²

Verified step by step guidance

Identify the given number in scientific notation: $3.8 \times 10^2$.

Understand that $10^2$ means moving the decimal point 2 places to the right.

Start with the number 3.8 and move the decimal point 2 places to the right.

After moving the decimal point, fill in any empty spaces with zeros if necessary.

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 formatted as a product of a number between 1 and 10 and a power of ten. For example, 3.8 x 10² means 3.8 multiplied by 100, which simplifies to 380.

Decimal Notation

Decimal notation is the standard way of writing numbers using digits from 0 to 9, where the position of each digit represents a power of ten. Converting from scientific notation to decimal notation involves calculating the value of the exponent and adjusting the decimal point accordingly. This process allows for a clearer understanding of the magnitude of the number.

Exponent Rules

Exponent rules are mathematical guidelines that dictate how to handle numbers raised to a power. In the context of scientific notation, the exponent indicates how many places to move the decimal point. A positive exponent means moving the decimal to the right, while a negative exponent would mean moving it to the left, which is essential for converting to decimal notation.