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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1:54 minutes

Problem 27

Textbook Question

In Exercises 15–30, write each number in scientific notation.0.007

Verified step by step guidance

Identify the decimal number that needs to be converted to scientific notation: 0.007.

Move the decimal point to the right until you have a number between 1 and 10. In this case, move the decimal point 3 places to the right to get 7.

Count the number of places you moved the decimal point. Here, it is 3 places.

Since you moved the decimal to the right, the exponent will be negative. Therefore, the exponent is -3.

Write the number in scientific notation as \(7 \times 10^{-3}\).

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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 0.007 can be expressed as 7 x 10^-3, where 7 is the coefficient and -3 indicates the decimal point has moved three places to the right.

Standard Form

Standard form refers to the conventional way of writing numbers, where the decimal point is placed after the first non-zero digit. In scientific notation, converting a number to standard form involves identifying the significant figures and determining the appropriate power of ten to represent the number accurately. This helps in simplifying calculations and comparisons.

Exponent Rules

Exponent rules are mathematical guidelines that govern the operations involving powers of ten. Key rules include multiplying powers by adding exponents and dividing powers by subtracting exponents. Understanding these rules is essential when manipulating numbers in scientific notation, as they help in simplifying expressions and performing calculations efficiently.