Conversions, Rounding, Sig Figs…Oh MY!!!

Accuracy and Precision

Accuracy How close did you get to the true or accepted value?

Precision How close a series of measurements are to one another?

Error Deviation from the accepted value how much you “missed” by

Percent Error The amount you “missed” by, expressed as a percentage of the accepted value VExperimental - VAccepted VAccepted % Err = x 100%

% Error Practice Accepted Density of sucrose is 1.59 g/cm3 Your three experimental trails were: 1.40 g/cm3, 1.68 g/cm3, and 1.45 g/cm3 Use the equation on the previous slide to calculate the percent error of your trials. 11.9% 5.66% 8.80%

Significant Figures The numbers we use in science are measurements Significant figures result from our inability to measure precisely

Significant Figures All certain digits One final uncertain digit (estimated)

16.

16. 7 mL

“Sig Figs*” Made Easy *Significant Figures

If a decimal point is present: Pacific Atlantic Pacific Atlantic If a decimal point is present: If a decimal point is absent: Pacific Atlantic

Decimal point is present: Pacific Atlantic Decimal point is present: 4.3 0.000520 150.200 2 SF 3 SF 6 SF

Decimal point is absent: Pacific Atlantic Decimal point is absent: 3 SF 153 1 265 000 1 000 4 SF 1 SF

Adding and Subtracting 30.254 30.254 – 0.0125 30.2415 + 1.22 31.474  31.47  30.242

Multiplying and Dividing Sig figs limited by the least precise measurement Exact conversion factors do not limit sig figs 30.45 m x 1.3 m =39.585 m2  40. m2 4 SF 2 SF 2 SF

PRACTICE 1.35 m x 2.467 m = 55.46 g - 28.9 g = 1 035 m2  42 m = 3.33 m2 26.6 g 25 m

Page 23 DIMENSIONAL ANALYSIS

DIMENSIONAL ANALYSIS Treat units in calculations as if they were algebraic factors

DIMENSIONAL ANALYSIS Units must always be included in the results of calculations Units also help you to check your work as you go 36 + 16 = 1 weeks weeks year

Conversion Factor A ratio equal to one Used to convert from one dimensional unit to another

Examples 1000m = 1 km 1km/1000m or 1000m/1km Denisty = 2.5g/mL 2.5g/mL 1mL/2.5g

“How many meters are in 3.75 km?” THE PROBLEM “How many meters are in 3.75 km?”

STEP #1: Restate the Problem “How many meters are in 3.75 km?” ? m = 3.75 km

STEP #2: Begin with the Known Quantity ? m = 3.75 km 3.75 km

STEP #3: “ Make a Conversion Grid” ? m = 3.75 km 3.75 km 1

STEP #4: Find the Correct Units for the Conversion Factor ? m = 3.75 km Units to survive on top km m 3.75 km 1 Units to cancel on bottom* * opposite

STEP #5: Attach Numbers to Units ? m = 3.75 km 1 km = 1 000 m 1 000 m 3.75 km 1 km 1

? m = 3.75 km m STEP #6: Do the Math! = 1 000 3.75 km 1 km 1 OR Multiply 3.75 times (1 000  1) Multiply (3.75 x 1 000) then  1 OR

? m = 3.75 km m 3 750 m STEP #7: Tah-Dah! = 3.75 km 1 000 1 km 1 Don’t forget: Your answer must contain units!

How many . . . Millimeters in 1.574 meters Kilograms in 873 grams 1,125ft/min to mi/hr

How many… decaliters in 35 kL? mg in .258 hg km in 35800 m