Significant digits Objectives State the purpose of significant

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….

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. )

Examples of Sig zeros 5, 002 5600. . 30 Examples of NONsig zeros 0. 005 0. 03 30 50, 000 This number has a mix of significant and insignificant zeros: 0. 00300

Rules for counting significant digits: � 2300 Non-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. )

Counting significant digits: � 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.

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 x 10 -3 zeros here 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

Counting significant digits - Practice � 0. 00400 Non-zeros = significant! � 0. 00400 zeros here at the beginning of a number = insignificant � 0. 00400 zeros here 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.

Practice �Problems 1 -10 on your notes

�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 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.

Example: 350. 83 kg + 400. 0 kg 750. 83 kg 350. 83 2 decimal places 400. 0 1 decimal place Lowest # of decimal places =1 I need to round this to only one decimal place 750. 8 kg

Example: 2. 0 x 8000 16, 000 2. 0 2 significant figures 8000 1 significant figure LEAST? = 1 I need to round this to only one significant digit 1 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 � 81÷ 9. 0 = 9. 0 � 3. 456 – 2. 455= 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 Non-zeros = significant! � 23. 00 zeros here 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.

Example: 10. 75 – 0. 411 10. 339 10. 75 2 decimal places 0. 411 3 decimal places LEAST? = 2 I need to round this to only two decimal place! 10. 34