Accuracy, Precision, & Significant Digits Chemistry CP Accuracy, Precision, & Significant Digits

Objectives Define accuracy Define precision Compare accuracy & precision Use significant figures

Accuracy Accuracy refers to how closely a measurement matches the true or actual values To be accurate only requires the true value (bulls eye) & one measurement (for the arrow to hit the target) Highly accurate data can be costly and difficult to acquire

Precision Precision refers to the reproducibility of the measurement and exactness of description in a number. To decide on precision, you need several measurements (notice multiple arrow holes), and you do not need to know the true value (none of the values are close to the target but all the holes are close together.)

Accuracy & Precision In order to be accurate and precise, one must pay close attention to detail to receive the same results every time as well as “hit the target”.

Comparing Accuracy & Precision Notice the difference in these pictures. To win the tournament the archers must hit the target the most times. The winner must show accuracy & precision. The 1st archer has _____ accuracy & ____ precision. The 2nd archer has _____ accuracy & ____ precision. The 3rd archer has _____ accuracy & ____ precision. The 4th archer has _____ accuracy & _____ precision BAD BAD BAD GOOD GOOD GOOD GOOD BAD

Example 1 A sample is known to weigh 3.182 g. Jane weighed the sample five different times with the resulting data. Which measurement was the most accurate? 3.200 g 3.180 g 3.152 g 3.189 g

Example 2 Consider the data (in cm) for the length of an object as measured by three students. The length is known to be 14.5 cm. Which student had the most precise work, and which student had the most accurate work? Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Student A 14.8 14.7 Student B 14.2 14.6 Student C 14.4 14.5

Solution Most precise: Student A (0.1 cm difference) Most accurate: Student C (2 were true value, rest within 0.1 cm) Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Student A 14.8 14.7 Student B 14.2 14.6 Student C 14.4 14.5

Significant Figures Why are significant figures necessary? True accuracy is no better than the measurement obtained by the least precise method. We use significant digits so we are not exaggerating our precision.

Rules of Significant Digits All digits 1 through 9 are significant. 9.342 mg = 4 Sig. Digits 233,124 = 6 sig. digits

Rules of Significant Digits 2. Zero is significant when it is between two non‐zero digits 2.06 = 3 SD 206 = 3 SD 100,001 = 6 SD

Rules of Significant Digits 3. Followers are good! A zero to the right of a decimal point in a number greater than or equal to one is significant. 1.000 (4 SD) 30.00 (4 SD) 205.0 (4 SD) 2.00000 (6 SD) 10.0 (3 SD)

Rules of Significant Digits 4. Leaders are losers. A zero to the right of a decimal point (in a number less than one) but to the left of nonzero digit is not significant. 0.001020 (4 SD) 0.00024200 (5 SD)

Rules of Significant Digits 5. No decimal no good. Zeros used only to space the decimal point (placeholders) are not significant. - 1000 (1 SD) - 1010 (3 SD) -78,000 (2 SD)

Counting SDs How many significant digits are in the following numbers? 1235 2020 235.0 0.0270 235 0.00010900 65,100 19,620,000,000 102, 800

Estimated to the tens place Estimated to the tenths place Why are S.F.s Important? When reporting a measurement the number of digits indicates the precision of an instrument. 100 ml Estimated to the tens place 99.9 mL Estimated to the tenths place

Why are S.F.s Necessary? When you divide 5.0 /0.87 = 5.7471… (Actual Answer: 5.7) S.F.s will provide a way to determine how many numbers to report in a measurement or calcualtion!

Example 1: How would you record this measurement? 1.37 cm

Example 2: Provide the measurements for each example. B.

How many significant digits would be recorded? 10 20 30 40 50 60 70 B. 10 20 30 40 50 60 70 C. 10 20 30 40 50 60 70

How many significant digits would be recorded? 48 cm (2 sfs) A. 10 20 30 40 50 60 70 B. 48 cm (2 sfs) 10 20 30 40 50 60 70 C. 48.0 cm (3 sfs) 10 20 30 40 50 60 70