2What is accuracy?The exactness of a measured number What? How close is the measurement to the true number That is accuracy
3What is Precision?Who closely grouped are is the data? The tighter the grouping the more precise. You can be precise and not accurate You can be accurate and not precise
4Sig Fig Rules Sig Figs only apply to measured data Are counted numbers measured?What about ratios?
5Sig Fig Rules ALL nonzero digits are significant What numbers are included in that statementALL whole numbers that are not zero
6Sig Fig Rules All zeros between nonzero digits are significant For example1003 has 4 sig figs7.301 has 4 sig figs30201 has 5 sig figs
7Sig Fig Rules ALL trailing zeros after a decimal are Significant Examples30.0 has 3 sig figshas 12 sig figs
8Sig Fig Rules ALL leading zeros are NOT significant Examples 011 has 2 sig figs0.011 has 2 sig figshas 3 sig figs
9Sig Fig Rules If no decimal is present, trailing zeros are NOT significantExamples1500 has 2 sig figshas 2 sig figs
10Sig Fig Rules Scientific notation shows ONLY sig figs Examples 1.50 x 103 has 3 sig figs4.567 x 108 has 4 sig figs1.00 x has 3 sig figs
11Sig Fig Rules A decimal following a zero makes all zeros SIGNIFICANT Examples10. has 2 sig figshas 5 sig figshas 15 sig figs
12Sig Fig RulesDo you want more rules?ME EITHERLet’s make it easier
13MY Sig Fig Rules If it ain’t zero count it If zero is trapped count it If zero follows numbers after zero and after a decimal, count itIf zero leads forget about it
14PracticeDetermine the number of significant digits in each of the following:6.571 g0.157 kg0.106 cmmm28.0 mlg2.690 g2500 mg
15Adding and subtracting The sum or difference cannot be more significant than the least precise measurement.HUH?!The answer can only have as many sig figs as the smallest number (in terms of sig figs)
17Multiplication and Division The product or quotient of measured data cannot have more sig figs than the least precise measured data.HUH?!The answer cannot have more sig figs than the smallest measured number (in terms of sig figs)
18Practice2.6 x 3.78 = ?6.54 x 0.37 = ?3.15 x 2.5 x 4.00 = ?0.085 x x = ?35 / 0.62 = ?39 / 24.2 = ?3.76 / 1.62 = ?0.075 / = ?
19Compound Calculations If the operations in a compound calculation are all of the same kind (multiplication/division OR addition/subtraction) complete the operations simultaneously using standard order of operations before rounding to the correct number of significant figures. Do ALL the MATH 1st and then round
20Compound Calculations If a solution to a problem requires the combination of both addition/subtraction and multiplication/division operations, rounding the intermediate solutions may introduce excess rounding answersFor intermediate calculations, you should underline the estimated digit in the result and retain at least one extra digit beyond the estimated digit. Drop all remaining numbers and do not roundRound the final calculation to the correct sig fig according to the applicable math rules taking into account the underlined estimated digits in the intermediate answers.
21Compound Calculations If the math is not the same then do all the same stuffTake the answer, go one number beyond the required sig fig, drop all other numbersFinish the mathUse sig fig rules for final answer
22ExampleThree students are assigned the task of calculating the total floor area of the school’s science lab. The first student finds that the area of the main lab floor is 9.3 m by 7.6 m. Meanwhile, the second student measures the floor area of the chemical storage area to be 3.35 m by 1.67 m. The third student determines that the closet floor area is 93.5 cm by cm. What is the total floor area in square meters?
23Trigonometry Angles are measured in radians in SI Radians are considered non-measured numbersDegrees follow same procedure (round to nearest tenth of a degree)Follow rules when converting