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 82

Textbook Question

In Exercises 77–86, write each number in scientific notation. −3829

Verified step by step guidance

Identify the significant digits in the number, which are 3829.

Determine the position of the decimal point in the original number. Since it's a whole number, the decimal is after the last digit: 3829.

Move the decimal point to the left until only one non-zero digit remains to the left of the decimal. For 3829, move the decimal 3 places to the left to get 3.829.

Count the number of places the decimal point was moved. In this case, it was moved 3 places.

Express the number in scientific notation as \(-3.829 \times 10^3\), where the exponent is positive because the original number is greater than 1.

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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 3829 can be expressed as 3.829 × 10^3 in scientific notation.

Negative Numbers in Scientific Notation

When writing negative numbers in scientific notation, the process is similar to positive numbers, but the coefficient remains negative. For instance, the number -3829 would be expressed as -3.829 × 10^3, indicating that it is a negative value while still adhering to the scientific notation format.

Standard Form Conversion

Converting a number to scientific notation involves identifying the significant figures and determining the appropriate power of ten. This requires moving the decimal point in the number until only one non-zero digit remains to its left, which helps in simplifying calculations and comparisons in scientific contexts.