Imagine you have a super large number like 3,000,000. Using scientific notation, we express this as a number between 1 and 10 multiplied by a power of 10. In the case of 3,000,000, we can write it as 3 X 10⁶. The 6 represents the number of zeros in the original number.

Now let’s look at a really small number, like 0.000005. In scientific notation, and once again we express this as a number between 1 and 10 multiplied by a power of 10. For 0.000005, it becomes 5 X 10⁻⁶. The -6 indicates that the decimal point moves six places to the left.

Here’s a step-by-step guide on how to convert a number in scientific notation:

1. Identify the non-zero digitals in the original number. For examples, in 4,500, it would be 4 and 5.
2. Write these digits as a number between 1 and 10. In our examples, it’s 4.5.
3. Determine the power of 10. Count how many places you moved the decimal point to get your number from the original. If you move to the left, the power is positive; if you move to the right, the power is negative.
4. Express the number in scientific notation. Combine the number from Step 2 with the power of 10 from Step 3. For example, 4,500 in scientific notation is 4.5 X 10³.

Here’s another good example of scientific notation using numbers: Scientists estimate that the weight of the Earth is 6,000,000,000,000,000,000,000,000,000kg. Can you imagine having to write this over and over for an equation or series of equations? It would take a lot of extra time and energy for the mathematician. So using scientific notation, we can write this number in a short-form way. This number can be written as 6 X 10²³. Much easier to write this down don’t you think?

We hope this helps you understand how and why we use scientific notation in algebra. Remember, never be afraid to ask questions!