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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1:47 minutes

Problem 76

Textbook Question

In Exercises 65–76, write each number in decimal notation without the use of exponents. −7.00001×10^10

Verified step by step guidance

Identify the given number in scientific notation: \(-7.00001 \times 10^{10}\).

Understand that the exponent 10 indicates how many places to move the decimal point.

Since the exponent is positive, move the decimal point 10 places to the right.

Start with the number \(-7.00001\) and move the decimal point 10 places to the right, adding zeros as needed.

Write the resulting number in decimal notation without exponents.

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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 to be conveniently written in decimal form. It is typically formatted as a product of a number between 1 and 10 and a power of ten. For example, the number 5,000 can be written as 5.0 × 10^3. Understanding this notation is essential for converting numbers into standard decimal form.

Decimal Notation

Decimal notation is the standard way of writing numbers using the base-10 system, which includes digits from 0 to 9. It represents whole numbers and fractions using a decimal point. For instance, the number 2.5 in decimal notation indicates two whole units and five-tenths. Converting from scientific notation to decimal notation requires careful placement of the decimal point based on the exponent.

Negative Numbers

Negative numbers are values less than zero, represented with a minus sign (-). In the context of scientific notation, a negative coefficient indicates that the number is in the negative range. For example, in the expression -7.00001 × 10^10, the negative sign indicates that the resulting decimal will also be negative. Understanding how to handle negative values is crucial when converting to decimal notation.