3.454 x 106
For very small numbers, you move the decimal point to the right until only one digit remains to the left of the decimal point. The number of moves to the right gives you a negative exponent:
5.234 x 10-7
Addition Example Using Scientific Notation
Addition and subtraction problems are handled the same way.
- Write the numbers to be added or subtracted in scientific notation.
- Add or subtract the first part of the numbers, leaving the exponent portion unchanged.
- Make sure your final answer is written in scientific notation.
3.2 x 103
Subtraction Example Using Scientific Notation
(5.3 x 10-4) - (2.2 x 10-4) =
3.1 x 10-4
Multiplication Example Using Scientific Notation
You do not have to write numbers to be multiplied and divided so that they have the same exponents. You can multiply the first numbers in each expression and add the exponents of 10 for multiplication problems.
(2.3 x 105)(5.0 x 10-12) =
When you multiply 2.3 and 5.3 you get 11.5. When you add the exponents you get 10-7. At this point your answer is:
11.5 x 10-7
You want to express your answer in scientific notation, which has only one digit to the left of the decimal point, so the answer should be rewritten as:
1.15 x 10-6
Division Example Using Scientific Notation
In division, you subtract the exponents of 10.
(2.1 x 10-2) / (7.0 x 10-3) =
0.3 x 101 =