Scientific and Standard Notation

Why do we use Scientific Notation Used to make very large (or small) confusing numbers easy to read. Used to make very large (or small) confusing numbers easy to read.

Scientific Notation Written in the form of M X 10 n M is a number between 1 and 9.999…..but not 10!! “N” is the number of times we move the decimal

+N Tells us it’s a number >1 (Large number) Move the decimal to the right. 4.6 x N Tells us it’s a number <1 (Small number) Move the decimal to the left. 4.6 x 10 -5

Examples Distance between the Earth to the nearest star Distance between the Earth to the nearest star 40,000,000,000,000 miles Diameter of a nucleus of an atom Diameter of a nucleus of an atom centimeters centimeters

Standard to Scientific Notation 40,000,000,000,

Scientific to Standard Notation Average distance between the Earth and Sun 1.49 x km = _________________________ km 149,000,000,000.0 km

Scientific to Standard Notation 0.2 x = _________________________

Common Numbers We See

Quick Review: Put these values into Scientific Notation: – 6,870,000 – – 2.0 Put these values into Standard Notation: – 4.6 X 10 9 – 7.86 X – 3.2 X 10 0

a)What is % Error? 1.How far from the true or accepted answer my calculation is 2.How “ wrong ” I am 3.The percent error in my calculation or measurement b)Add formula to your ESRT p. 1 (equations box) c)Used to evaluate the validity of a measurement or calculation

% Error = mv – av X 100 av mv = measured value av = accepted value

Practice…. 1.Mr. Babicz measured the height of his new bookcase to be 4.85 m. The manufacturer ’ s measurement of the bookcase ’ s height is 4.50 m. Calculate Mr. Babicz’s percent error: 1.The actual density of water is 1.0 g/mL. A student measured the density to be 1.14 g/mL. What is the percent error of this calculation?