To add numbers in scientific notation, convert all numbers so they have the same exponent as the largest number, add the new coefficients and convert the answer so it is in scientific notation. If the numbers begin with the same exponent, add the coefficients and convert the answer, if necessary.
- Convert all numbers to have the same exponent
Since the base in scientific notation is always 10, it is only necessary to convert the exponents. Move the decimal point one place to the left, adding leading zeros as necessary for each increase of 1 in the exponent.
- Add the coefficients
Use simple addition to find the sum of the converted coefficients. The base and exponent remain the same, and you carry them to the answer.
- Convert the answer to scientific notation
In scientific notation, the coefficient is always a number between 1 and 10. If the sum of the numbers you are adding is greater than 10, you must convert the answer so the coefficient fits these parameters. Convert the number to scientific notation by moving the decimal point to the left, and increase the exponent by one for each move of the decimal point. Round the answer to the correct number of significant digits.