How to use scientific notation?
The main logic behind using scientific notation is to take a very large or small number and convert it to an easy to read/write expression. For an example that isn't a power of 10, the number 0.5 converted to scientific notation would read as 5 * 10^-1. We reached this expression by moving the decimal point in 0.5 once to the right-hand side making the number into 5. The goal of using scientific notation is to reach the base number, meaning a number between 1 and 9. As we had to move the decimal point to the right-hand side, we know that the expression would read as a negative exponent, whereas if we were to move the decimal point to the left-hand side, the exponent would be positive. The number 5 is our base, and we multiply it by 10 with an exponent that is equal to the number of times we moved the decimal point to reach the said base. In our case, it would be 1. Lastly, we know that the exponent would be negative because we are dealing with 0.5, a number less than 1, and we had to move the decimal point to the right-hand side. As a result, our scientific notation of 0.5 would be 5 * 10^-1. Here are a few more examples of large and small numbers as expressed in the scientific notation:
- 642,300,544,000 – 6.42300544 * 10^11
- .00002055 – 2.055 * 10^-5
- 8,549,248.5004 – 8.549285004 * 10^6
- .0125174 – 1.25174 * 10^-2
