Scientific Notation Ch 3 Scientific Notation We use

Scientific Notation Ch. 3

Scientific Notation • We use scientific notation because we deal with very large and very small numbers. • Scientific notation is written as a product of 2 numbers. The first is a coefficient, and the second is 10 raised to a power called an exponent. Coefficient is always a number greater than 1 and less than 10. The exponent equals the number of places the original decimal point has been moved to write in scientific notation.

Scientific Notation • When moving the decimal to the left, the exponent is positive Ex. 1 36, 000 is written as 3. 6 X 104 • When moving the decimal to the right, the exponent is negative Ex. 2 0. 0081 is written as 8. 1 X 10 -3

Multiplying using scientific notation • To multiply, simply multiply the coefficients and add the exponents Ex. (3. 0 X 104) x (2. 0 X 102) (3. 0 x 2. 0) X 10 4+2 6. 0 X 106

Dividing using scientific notation • To divide, simply divide the coefficients and subtract the exponents. • Ex. (3. 0 X 104) / (2. 0 X 102) (3. 0 / 2. 0) X 10 4 -2 1. 5 X 102

Addition or subtraction using scientific notation • To add or subtract, the exponents must be made to be the same. This is like lining up the decimal when we add or subtract. Ex. (5. 40 X 103) + (6. 0 X 102) First, make the exponent the same (5. 40 X 103) + (. 60 X 103) Now just add or subtract the coefficients (5. 4 +. 60) X 103 = 6. 0 X 103