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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1:33 minutes

Problem 33

Textbook Question

Write each number in decimal notation: 7.45*10^(-5)

Verified step by step guidance

Understand the problem: The given number is written in scientific notation, which is a way to express very large or very small numbers. The goal is to convert it into standard decimal notation.

Identify the components of the scientific notation: The number is written as 7.45 × 10^(-5). Here, 7.45 is the coefficient, and 10^(-5) indicates that the decimal point needs to be moved 5 places to the left because the exponent is negative.

Move the decimal point: Start with the coefficient 7.45. To move the decimal point 5 places to the left, add zeros as placeholders to the left of the number.

Write the result: After moving the decimal point 5 places to the left, the number will be in standard decimal notation. Ensure the final result is written with the correct number of zeros and the decimal point in the correct position.

Double-check your work: Verify that the decimal point has been moved the correct number of places and that the result matches the original scientific notation.

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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, 7.45*10^(-5) means 7.45 divided by 100,000, which simplifies calculations and comparisons of very large or small values.

Decimal Notation

Decimal notation is the standard form of writing numbers using digits and a decimal point to separate the whole number part from the fractional part. It allows for a clear representation of values, including those that are fractions or very small numbers, such as 0.0000745 for 7.45*10^(-5). Understanding how to convert scientific notation to decimal notation is essential for interpreting numerical data.

Exponents

Exponents indicate how many times a number, known as the base, is multiplied by itself. In the expression 10^(-5), the base is 10, and the exponent is -5, which means 1 divided by 10 raised to the power of 5, or 1/100,000. Grasping the concept of exponents is crucial for manipulating and converting numbers in scientific notation.