Problem 106 - College Algebra

Question

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

Step-by-Step Solution

Answer

Decimal to scientific notation conversion involves identifying and moving the decimal point, and then determining power of 10. For example, 300.0 in decimal is written as \(3 \times 10^{2}\) in scientific notation.

Step 1: Identify The Decimal Point

For any given decimal number, the first step is to identify the position of the decimal point. If there are many digits present after the decimal point, round off to two decimal places for simplicity.

Step 2: Move the Decimal Point

This step involves moving the decimal point in the number to its new position right after the first non-zero number from the left. In this process, make sure to count the number of times you move the decimal point. This count is important and will be used to determine the exponent of 10.

Step 3: Determine the Exponent

Once you moved the decimal, it’s time to build the scientific notation. Start by writing down the number you now have, followed by a multiplication symbol and then 10 raised to a power. The power or exponent of 10 is the number of times you moved the decimal point. If you moved to the left, the number is positive. If you moved to the right, the number is negative.

Step 4: Example

Let's take 300.0 as an example. Here, we have to move the decimal point two places to the left to get 3. So, in scientific notation, 300.0 is written as \(3 \times 10^{2}\).