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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1:23 minutes

Problem 7

Textbook Question

In Exercises 1–14, write each number in decimal notation without the use of exponents.1.4X10⁰

Verified step by step guidance

Identify the given number in scientific notation: \(1.4 \times 10^0\).

Recall that any number raised to the power of 0 is 1, so \(10^0 = 1\).

Multiply the coefficient (1.4) by the result from the previous step (1).

Perform the multiplication: \(1.4 \times 1\).

Write the result as a decimal number.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Decimal Notation

Decimal notation is a way of expressing numbers using a base of ten, where each digit represents a power of ten. For example, the number 1.4 in decimal notation means 1.4 times ten to the power of zero, which is simply 1.4. Understanding how to convert numbers from scientific notation to decimal notation is essential for accurately interpreting and using numerical data.

Scientific Notation

Scientific notation is a method of expressing very large or very small numbers in a compact form, typically as a product of a number between 1 and 10 and a power of ten. In the example given, 1.4 x 10⁰ indicates that the number is 1.4 multiplied by 1 (since 10⁰ equals 1). Recognizing how to manipulate and convert scientific notation is crucial for solving problems in algebra.

Powers of Ten

Powers of ten are expressions that represent ten multiplied by itself a certain number of times, denoted as 10^n, where n is an integer. For instance, 10⁰ equals 1, 10¹ equals 10, and 10² equals 100. Understanding powers of ten is fundamental in both scientific notation and decimal notation, as it helps in determining the scale and value of numbers.