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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1:45 minutes

Problem 29

Textbook Question

In Exercises 15–30, write each number in scientific notation.3.14159

Verified step by step guidance

Identify the decimal point in the number 3.14159.

Move the decimal point to the right of the first non-zero digit, which is 3, resulting in 3.14159 becoming 3.14159.

Count the number of places the decimal point was moved. In this case, it was moved 0 places to the right.

Express the number in the form \( a \times 10^n \), where \( a \) is a number between 1 and 10, and \( n \) is the number of places the decimal was moved. Here, \( a = 3.14159 \) and \( n = 0 \).

Write the final expression in scientific notation as \( 3.14159 \times 10^0 \).

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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 3.14159 can be expressed as 3.14159 × 10^0, since it is already between 1 and 10.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient (the number between 1 and 10) are considered significant. For 3.14159, all five digits are significant, which is important for maintaining accuracy when converting to scientific notation.

Powers of Ten

Powers of ten are used in scientific notation to indicate the scale of the number. Each power of ten represents a factor of ten multiplied by itself. For instance, 10^1 equals 10, 10^2 equals 100, and so on. Understanding how to manipulate powers of ten is essential for converting numbers into scientific notation correctly.