Significant digits Objectives: State the purpose of significant digits State and apply the rules for counting and doing calculations with significant digits
One way engineers use significant digits…. Cupertino, CA
What's so significant about significant digits?
Significant digits Measurements that indicate the precision of the tool used Important—we want to let other scientists and engineers know how “good” our measurements are!
3.42 cm This means: My tool had markings to the tenths place (I can COUNT them) I estimated the hundredths place (the object was between 3.4 and 3.5 but closer to 3.4) 3 significant digits
3900 cm This means: My tool had markings to the thousands place (I could COUNT them) I estimated the hundreds place (the object was between 3000 and 4000 but much closer to 4000 ) 2 significant digits
3900. cm This means: My tool had markings to the tens place (I could COUNT them) I estimated the ones place (the object appeared to be right at 3900) 4 significant digits
Clues: How to know when a number is significant It is a non-zero (1, 2, 3, 4, 5, 6, 7, 8, 9) It is a zero at the END of a decimal AFTER a decimal point (4.500) It is a zero between non-zeros (5,005) It is a zero at the end of a whole number AND there is a decimal (50.) Practice probs for just this info – HW for 9/7
Examples of Sig zeros Examples of NON-sig zeros 5,002 5600. .30 0.005 0.03 30 50,000,000 This number has a mix of significant and insignificant zeros: 0.00300
Rules for counting significant digits: 2300 2300Non-zeros are significant 2300 zeros are at the end of a number without a decimal = insignificant 2300 = 2 s.f. This means the tool allowed us to COUNT the thousands place, and estimate the hundreds place (we counted to 2000 and we estimated the value was between 2000 and 3000, but closer to 2000.) I DO
Counting significant digits: 230. 230. Non-zeros = significant 230. zero here is at the end of a number WITH a decimal = significant 230. = 3 s.f This means the tool allowed us to COUNT to the ones place 230 and we estimated that the value was exactly at 230. WE DO. CHECK THIS
Counting significant digits: 2.300 x 10-3 BIG IDEA: count the digits of the coefficient only 2.300 x 10-3 Non-zeros = significant 2.300 x10-3 zeros here are at the end of a number and AFTER a decimal = significant 2.300 x 10-3 = 4 s.f. This means the tool allowed us to measure .00230, and we estimated it was exactly at .002300 YOU DO W PARTNER. CHECK
Counting significant digits - Practice 0.00400 0.00400 Non-zeros = significant! 0.00400 zeros here are at the beginning of a number = insignificant 0.00400 zeros here are at the end of a number and AFTER a decimal = significant 0.00400 = 3 s.f. This means the tool allowed us to measure 0.0040, and we estimated it was exactly at 0.00400. YOU DO ON OWN
Practice Problems 1-10 on your notes
Compare numbers – which is more precise and how do you know. Game – cc Compare numbers – which is more precise and how do you know. Game – cc. add this to prac probs Give practical example – ie 2 diff thermoms to meas the same temp
Practice - Answers State the number of significant digits. 1) 1234 4 1) 1234 4 2) 0.023 2 3) 890 2 4) 91010 4 5) 9010.0 5 6) 1090.0010 8 7) 0.00120 3 8) 3.4 x 104 2 9) 9.0 x 10-3 2 10) 9.010 x 10-2 4
Calculations: Addition and subtraction: USE lowest number of decimal places as the # of decimal places for your answer. Just do add probs in class maybe 1 subt. Prep to not have add and subt, and have it just in case Another day multiplying and dividing USE least number of total sig figs as the # of sig figs for your answer.
750.8 kg Example: 350.83 kg + 400.0 kg 350.83 2decimal places Lowest # of decimal places = 1 750.83 kg I need to round this to only one decimal place 750.8 kg
20,000 Example: 2.0 x 8000 2.0 2 significant figures LEAST? = 1 16,000 I need to round this to only one significant digit1 20,000
Practice Problems 11-20 in your notes
Practice - Answers 5.33 + 6.020 = 11.350 11.35 5.0 x 8 = 40.0 40 5.33 + 6.020 = 11.350 11.35 5.0 x 8 = 40.0 40 81÷ 9.0 = 9.0 9.0 3.456 – 2.455= 1.001 1.001 5.5 – 2.500 =3.000 3.0 7.0 x 200 =1400.0 1000 300. ÷ 10.0 = 3.0 3 (3.0 x 104)x (2.0 x 101) = 6.0 x 105 6.0 x 105 (9.000 x 10-2)÷ (3.00 x 101) = 3.000 x 10-3 3.00 x 10-3 (3.0 x 104) - (2.0 x 101) = 2.998 x 104 3.0 x 104
Exit Ticket
2300
Counting significant digits: 450.0 What do we know about the measurement made? How many significant digits are in the answer? Is this number more less precise than the previous answer?
Counting significant digits: 20 What do we know about the measurement made? How many significant digits are in the answer? Is this number more less precise than the previous answer?
Counting significant digits: 0.000450 What do we know about the measurement made? How many significant digits are in the answer? Is this number more less precise than the previous answer?
Counting significant digits: 3,006 What do we know about the measurement made? How many significant digits are in the answer? Is this number more less precise than the previous answer?
Counting significant digits: 23.00 23.00 Non-zeros = significant! 23.00 zeros here are at the end of a number and AFTER a decimal = significant 23.00 = 4 s.f. This means the tool allowed us to measure 23.0, and we estimated it was exactly at 23.0. YOU DO W PARTNER
10.34 Example: 10.75 – 0.411 10.75 2 decimal places LEAST? = 2 10.339 I need to round this to only two decimal place! 10.34 WE DO