Problem 130 - College Algebra

Question

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

Step-by-Step Solution

Answer

To convert a decimal number to scientific notation, move the decimal point to the right of the first non-zero digit, count the number of places moved and represent that as a power of 10, considering the original number's size. For 4500, scientific notation is \(4.5 \times 10^3\).

Step 1: Understand the concept of scientific notation

Scientific notation is a method of writing very large or very small numbers using powers of 10. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Step 2: Convert the decimal to scientific notation

To convert a number from decimal form to scientific notation, firstly locate the decimal point in the original number. Then shift the decimal point to the right of the first non-zero digit. This forms a number between 1 and 10, considered as \(a\). Count the number of places the decimal point was moved, this is called \(n\). If the original number was less than 1, then \(n\) is negative. If the original number is greater than 1, then \(n\) is positive.

Step 3: Example

Let's consider a number, for example, 4500. Firstly, locate the decimal point, it's at the end of the number (4500.). Next, move the decimal place to the right of the first non-zero digit, making it 4.5. The decimal was moved 3 places to the left, hence \(n=3\). This makes the scientific notation \(4.5 \times 10^3\).