Sig Figs

Scientific Notation In science, we often come across either very large or very small numbers, so we use Scientific Notation as a way to simplify them. Some numbers hard to work with: Mass of one atom = kg # atoms in 2 grams of hydrogen = atoms

Scientific Notation Easier: Mass of one electron = 9.1 x # atoms in 2 g hydrogen = 1.2 x 10 24

In Scientific Notation, a number is written as the product of two numbers: A coefficient, and 10 raised to a power (exponent). The coefficient is always greater than or equal to 1, and less than 10 M x 10 n M = Coefficient between 1 and is the base n is the exponent

Scientific Notation Worksheet Numbers > 1 have a positive exponent 5.2 x 10 3 Numbers < 1 have a negative exponent 9.65 x 10 -4

The Importance of Measurement Ex: converted to scientific notation: In this case: In order for the coefficient to be between 1 and 10, the decimal has to move 3 places to the left. The decimal moved 3 times, so the value of the exponent is 3 The number (2011) is bigger than 1, so the exponent will be positive. (10 3 = 1000., so this reads x 1000 which = 2011.) Ex: converted to scientific notation: In this case: In order for the coefficient to be between 1 and 10, the decimal has to move 2 places to the right. The decimal moved 2 times, so the value of the exponent is 2 The number (0.036) is less than 1, so the exponent will be negative. (10 -2 = 0.01, so this reads 3.6 x 0.01 which = 0.036) 2.011x x 10 -2

The Importance of Measurement x x 10 6 Convert the following numbers from standard to scientific notation Convert the following numbers from scientific to standard notation 7.29 x x Practice

Significant Figures We keep track of measurement accuracy through significant digits(Sig Digs) also called significant figures (Sig. Fig) A measurement is considered to be more accurate if it has more significant digits Significant Figures = all known digits plus one estimated digit

Significant Figures RULES 1) No zeros? All significant ) All sandwich zeros significant ) Leading zeros are not significant ) If digits are left of a decimal then zeros right of a decimal are significant3.00 5) Scientific notation indicates significant figures when numbers end in zero 300 = 3 x 10 2 or 3.00 x 10 2 When you have to guess, zeros don’t count

Uncertainty in Measurements Practice: Count the number of significant digits in each measurement meters8.750 x centimeters 8765 seconds 200. yards milliliters200 yards200.0 yards grams milliseconds

Uncertainty in Measurements Accuracy is a measure of how close the measurement is to the actual, or “true value” of what was measured. Actual blood glucose level = mg/dL

Uncertainty in Measurements Precision is a measure of how close your measurements are to each other. -measurements do not have to be accurate to be precise -measurements can be both precise and accurate, or neither.