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Chapter 5: Problem 149

Explain how to convert from scientific to decimal notation and give an example.

Short Answer

Expert verified
To convert from scientific to decimal notation, start with the number before the multiplication sign and move the decimal point the number of places indicated by the power of ten. Move it to the right for positive powers and to the left for negative powers.

Step by step solution

01

Understand the Concept of Scientific Notation

Scientific notation is a method for expressing very large or very small numbers in a compact form. A number in scientific notation is expressed as \(a 脳 10^n\) where \(a\) is a number between 1 and 10 and \(n\) is an integer, positive for numbers greater than 1 and negative for fractional numbers.
02

Conversion Method Explanation

To convert from scientific notation to decimal, start with the component \(a\) and move the decimal point to the right if \(n\) is positive and the equivalent positions to the left if \(n\) is negative.
03

Example of Conversion

Consider \(2.5 脳 10^3\) in scientific notation. To convert it to decimal notation, start with \(2.5\) and move the decimal point 3 places to the right, as the 3 in \(10^3\) indicates (since 3 is positive). This yields \(2500\) in decimal notation. Similarly, to convert \(3.14 脳 10^{-2}\) to decimal notation, start with \(3.14\) and move the decimal point 2 places to the left, as the -2 in \(10^{-2}\) indicates (since -2 is negative). This yields \(0.0314\) in decimal notation.

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