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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2:09 minutes

Problem 15

Textbook Question

In Exercises 15–30, write each number in scientific notation.32,000

Verified step by step guidance

Identify the significant figures in the number 32,000. In this case, the significant figures are 3.2.

Determine the power of 10 needed to express the number in scientific notation. Count how many places you move the decimal point to the left to get from 32,000 to 3.2. This is 4 places.

Express the number in the form \( a \times 10^n \), where \( a \) is a number greater than or equal to 1 and less than 10, and \( n \) is an integer. Here, \( a = 3.2 \) and \( n = 4 \).

Combine the significant figures and the power of 10 to write the number in scientific notation: \( 3.2 \times 10^4 \).

Verify that the scientific notation correctly represents the original number by expanding \( 3.2 \times 10^4 \) back to 32,000.

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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 32,000 can be expressed as 3.2 x 10^4, where 3.2 is the coefficient and 10^4 indicates that the decimal point in 3.2 is moved four places to the right.

Standard Form

Standard form refers to the conventional way of writing numbers without exponents. In this context, it is the regular representation of numbers like 32,000. Understanding how to convert from standard form to scientific notation is essential, as it involves identifying the significant figures and the appropriate power of ten.

Exponent Rules

Exponent rules are mathematical guidelines that govern the operations involving powers of numbers. When converting to scientific notation, it is important to understand how to manipulate exponents, such as multiplying or dividing powers of ten. For instance, moving the decimal point to the left increases the exponent, while moving it to the right decreases it.