2.5 Notes – Scientific Notation

Scientific Notation Scientific Notation – Shorthand for large numbers. Move the decimal so only one non-zero digit is to the left of the decimal. (If the number is larger than one, the decimal moves to the left; smaller than one, the decimal moves to the right.) The exponent will be positive if the number is larger than one and negative if less than one. Sample problems – Remember to retain significance when changing measurements to the expanded form.

Convert the following quantities to scientific notation. 700. m b. 5,000,000,000 kg c. 0.00023 kg d. 0.000 000 80 cm

2. Calculating with scientific notation a. Rules – when multiplying, exponents should be added together; when dividing, exponents should be subtracted; use the EE button and start doing the problem in one step

Sample Problems 1. (2 X 10-4 cm) X (3 X 102 cm) 2 X 3 = 6 and 10-4 + 102 = 10-2  6 X 10-2   2. (8 X 104 g) ÷ (4 X 101 cm) 8 / 4 = 2 and 104 – 101 = 103  2 X 103

Sample Problems 3. What is the speed of an object traveling 400m in 0.02 sec? 400/.02 = 4 X 102/2 X 10-2 = 4/2 = 2 and 2- (-2) = 4  2 X 104m/s   4. A very large square measures 4, 000cm by 10,000cm. What is the area? 4,000 X 10,000 = (4 X 103) X (1 X 104) = 4 X 107 cm2