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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1:43 minutes

Problem 86

Textbook Question

In Exercises 77–86, write each number in scientific notation. −0.00000000405

Verified step by step guidance

Identify the decimal point in the number -0.00000000405.

Move the decimal point to the right until you have a number between 1 and 10. In this case, move it 9 places to the right to get 4.05.

Since you moved the decimal 9 places to the right, the exponent will be -9.

Combine the number 4.05 with the power of 10 to express the number in scientific notation.

The scientific notation of the number is -4.05 \times 10^{-9}.

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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 4,500 can be expressed as 4.5 × 10^3. This notation simplifies calculations and comparisons of very large or very small values.

Negative Exponents

Negative exponents indicate that the base number should be divided rather than multiplied. For instance, 10^-3 means 1 divided by 10 raised to the power of 3, or 1/1000. In scientific notation, negative exponents are often used to represent very small numbers, such as 0.00000405, which can be expressed as 4.05 × 10^-9.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When converting to scientific notation, it is important to maintain the correct number of significant figures to accurately represent the original number's precision, such as ensuring that 4.05 retains its significant figures when expressed as 4.05 × 10^-9.