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Chapter 0: Problem 128

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

Short Answer

Expert verified
The conversion from decimal to scientific notation involves placing the decimal point of the number such that there is a single non-zero digit to its left, counting the number of decimal places moved as exponent 'n', and writing the number in the form \(a x 10^n\). For example, 300 in scientific notation is written as \(3.00 x 10^2\).

Step by step solution

01

Understanding Decimal and Scientific Notation

Before starting with the transformation, one must know what both forms are. Decimal notation is simply the standard way of writing down numbers. On the other hand, Scientific notation is a way to express very large or very small numbers in the form of \(a x 10^n\), where 1 鈮� |a| < 10 and n represents the number of times 10 is multiplied by itself.
02

Procedure for Converting to Scientific Notation

To convert a number from decimal notation to scientific notation, follow these steps: Step 1 - Place the decimal point such that there is only one non-zero digit to its left. This will give you the decimal part 'a' in the scientific notation. Step 2 - Count the number of places the decimal point had to be moved. This will give you the exponent part 'n' in the scientific notation. If the original number was less than 1, then n should be negative. If the original number was greater than 1, then n will be positive.
03

Example

Let's take an example by using the number 300. Step 1 - Moving the decimal point two positions to the left gives 3.00. So, a = 3. Step 2 - The decimal moved two positions from the original position and the number is greater than 1. So, n = 2. Therefore, 300 in scientific notation is written as \(3.00 x 10^2\).

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