SIGNIFICANT FIGURES & SCIENTIFIC NOTATION

1. SIGNIFICANT FIGURES & SCIENTIFIC NOTATION Sig Figs

2. 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 = 0.000000000000000000000000000000091 kg # atoms in 2 grams of hydrogen =1200000000000000000000000 atoms

3. Scientific Notation Easier: Mass of one electron = 9.1 x 10-32 # atoms in 2 g hydrogen = 1.2 x 1024

4. 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 10n M = Coefficient between 1 and 10 10 is the base n is the exponent

5. Scientific Notation Worksheet Numbers > 1have a positive exponent 5.2 x 103 Numbers < 1 have a negativeexponent 9.65 x 10-4

6. The Importance of Measurement 2.011 x 10 3 + Ex: 2011. 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. (103 = 1000., so this reads 2.011 x 1000 which = 2011.) Ex: 0.036 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 x 10 3.6

7. The Importance of Measurement Practice Convert the following numbers from standard to scientific notation 2 000 000. 0.000 000 001 420 2 x 106 1.420 x 10-9 Convert the following numbers from scientific to standard notation 7.29 x 1015 9.25 x 10-11 7 290 000 000 000 000. 0.000 000 000 092 5

23. Significant Figures We keep track of measurement accuracy through significant digits(SigDigs) 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

24. Significant Figures RULES • No zeros? All significant. 377 • All sandwich zeros significant. 307 • Leading zeros are not significant. 0.00312 • If digits are left of a decimal then zeros right of a decimal are significant 3.00 • Scientific notation indicates significant figures when numbers end in zero • 300 = 3 x 102 or 3.00 x 102 • When you have to guess, zeros don’t count

25. Uncertainty in Measurements Practice: Count the number of significant digits in each measurement. 0.05730 meters 8.750 x 10-2 centimeters 8765 seconds 200. yards 0.00073 milliliters 200 yards 200.0 yards 40.070 grams 101010 milliseconds 4 4 4 3 2 1 4 5 5

26. 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 = 94.899 mg/dL

27. 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.