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Chapter 0: Problem 127

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

Short Answer

Expert verified
First, understand the structure of scientific notation which is \(a \times 10^n\). To convert to decimal notation, shift the decimal point in \(a\) by \(n\) positions to the right if \(n\) is positive, or left if \(n\) is negative. For example, \(3.5 \times 10^3\) becomes \(3500.0\).

Step by step solution

01

Understand Scientific Notation

Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in decimal form. It's expressed as a number between 1 and 10 (let鈥檚 denote it as \(a\)) multiplied by a power of 10 (denoted as \(10^n\)), where \(n\) is an integer. So, it typically looks like this: \(a \times 10^n \).
02

Conversion Method

To convert from scientific notation to decimal notation, the given numerical expression \(a \times 10^n\) will be converted by moving the decimal point in \(a\) to the right if \(n\) is positive (which expresses a large number) and to the left if \(n\) is negative (which expresses a small number). The amount of positions you move the decimal point is equal to the absolute value of \(n\).
03

Give an Example

For instance, consider the number \(3.5 \times 10^3\) in scientific notation. As the value of \(n\) is positive 3, move the decimal point in \(3.5\) to the right 3 places. If there are not enough digits, you can append zeroes. So, \(3.5 \times 10^3\) would become \(3500.0\) in decimal notation.

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