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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
3000 can be expressed in scientific notation as \(3 \times 10^3\).

Step by step solution

01

Understand Scientific Notation

Scientific notation is a method of writing very large or very small numbers. A number in scientific notation is represented as \(a \times 10^n\) where \(a\) is a number between 1 and 10 (including 1 but excluding 10) and \(n\) is an integer.
02

Conversion to Scientific Notation

To convert from decimal to scientific notation, start by moving the decimal point in the number to create a new number between 1 and 10. count how many places you've moved the decimal point. This number is \(n\), the exponent.
03

Determine the Exponent's Sign

If the original decimal was less than 1, then \(n\) is negative. If the original decimal was greater than 1, then \(n\) is positive.
04

Write in Scientific Notation

Use the new number and the value of \(n\) to express the original number in scientific notation.
05

Example Conversion

Take 3000 for example. First, move the decimal point, it's currently at the end of the number, to after the first digit. You have 3.000, which can be more simply written as 3. Next, count the places you moved the decimal point. You moved it three places. So, the original number can be expressed in scientific notation as \(3 \times 10^3\).

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