Using Scientific Measurements Section 2.3

Accuracy and Precision Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

A measurement was taken three times. The correct measurement was 68 A measurement was taken three times. The correct measurement was 68.1 mL.  Circle whether the set of measurements is accurate, precise, both, or neither. 1. 78.1 mL, 43.9 mL, 2.0 mL                              accurate       precise       both       neither 2. 68.1 mL, 68.2 mL, 68.0 mL                            accurate       precise       both       neither 3. 98.0 mL, 98.2 mL, 97.9 mL                            accurate       precise       both       neither

Percent Error The accuracy of an individual value or of an average experimental value can be compared quantitatively with the correct or accepted value by calculating the percentage error.

Sample problem  A student measures the mass and volume of a substance and calculated its density as 1.40 g/mL. The corret or accepted value of the density is 1.30 g/mL. What is the percentage error of the student's measurement?

Error in Measurement Every experimental measurement has a degree of uncertainty. The volume, at the right is certain in the 10’s place, Greater than 10ml and less than 20ml The 1’s digit is also certain, greater than 17ml and less than 20ml. A best guess is needed for the tenths place.

Precision and Instruments Do all measuring devices have the same amount of precision?

Ex: The scale on the left has an uncertainty of (+/- .1g) You indicate the precision of the equipment by recording its Uncertainty Ex:  The scale on the left has an uncertainty of (+/- .1g) Ex:  The scale on the right has an uncertainty of   (+/- .01g)

Significant Figures In Science, measured values are reported in terms of significant figures. Significant figures in a measurement include all of the known digits plus one estimated digit.

For example… Look at the ruler below Each line is 0.1cm You can read that the arrow is on 13.3 cm However, using significant figures, you must estimate the next digit That would give you 13.30 cm

Let’s try this one Look at the ruler below What can you read before you estimate? 12.8 cm Now estimate the next digit… 12.85 cm

Rules for Determining Significant Zeros How many significant digits are in the following numbers? 274 25.632 8.988 Rule #1 All non zero digits are ALWAYS significant

Rules for Determining Significant Zeros How many significant digits are in the following numbers? 507 60007 9.088 Rules for Determining Significant Zeros Rule #2. All zeros between significant digits are ALWAYS significant

Rules for Determining Significant Zeros How many significant digits are in the following numbers? 32.0 19.000 105.0020 Rules for Determining Significant Zeros Rule #3 All FINAL zeros to the right of the decimal ARE significant

Rules for Determining Significant Zeros How many significant digits are in the following numbers 0.0002 0.000000789 Rules for Determining Significant Zeros Rule #4 All zeros that act as place holders are NOT significant Another way to say this is: zeros are only significant if they are between significant digits OR are the very final thing at the end of a decimal.

Determine the number of significant figures in each of the following. 0.014 403 0 km 1002 m 400 mL 30 000. Cm 0.000 625 000 kg

B) 4 significant figures C) 6 significant figures Suppose the value "seven thousand centimeters" is reported to you. How should the number be expressed if it is intended to contain the following? A) 1 significant figure B) 4 significant figures C) 6 significant figures

Do Now How many significant figures are in each of the following measurements? A) 0.4004 mL 4 SF B) 6000 g 1~4 SF C) 1.000 30 km 6 SF D) 400. mm 3 SF

Rules for Rounding numbers # 1 •If the digit to the immediate right of the last significant digit is greater than 5, you round up the last significant figure •Let’s say you have the number 234.87 and you want 4 significant digits •234.87 – The last number you want is the 8 and the number to the right is a 7 •Therefore, you would round up & get 234.9

Rules for Rounding numbers # 2 •If the digit to the immediate right of the last significant digit is less than 5, do not round up the last significant digit. •For example, let’s say you have the number 43.82 and you want 3 significant digits •The last number that you want is the 8 – 43.82 •The number to the right of the 8 is a 2 •Therefore, you would not round up & the number would be 43.8

Rules for Rounding numbers # 3 •If the number to the immediate right of the last significant is a 5, and that 5 is followed by a non zero digit, round up •78.657  (you want 3 significant digits) •The number you want is the 6 •The 6 is followed by a 5 and the 5 is followed by a non zero number •Therefore, you round up •78.7

Rules for Rounding numbers # 4 •If the number to the immediate right of the last significant is a 5, and that 5 is followed by a zero, you look at the last significant digit and make it even. •2.5350  (want 3 significant digits) •The number to the right of the digit you want is a 5 followed by a 0 •Therefore you want the final digit to be even •2.54

Rules for Rounding numbers # 5 •2.5250    (want 3 significant digits) •The number to the right of the digit you want is a 5 and it is not follow by a non-zero digit , and the preceding digit is even the last digit stays the same •2.52

Addition or Substraction with significant figures When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. 2.03 g+25.1g= 27.13g        27.1g When working with whole numbers the answer should be rounded so that the final significant digit is in the same place as the leftmost uncertain digit. 5400+365= 5800

Multiplication or substraction with significant figures The answer can have no more significant figures than are in the measurement with the fewest number of significant figures. 3.05 g/ 8.47 g =0.360094451 g           0.360g

Practice Problems What is the sum of 2.009 g and 0.05681 g ? Calculate the quantity 87.3 cm – 1.655 cm. Calculate the area of a rectangular crystal surface that measures 1.34 µm by 0.7488 µm (Area= length x with) Polycarbonate plastic has a density of 1.2 g/cm³. a photo frame is constructed from two 3.0 mm sheets of polycarbonate. Each sheet measures 28 cm by 22 cm. what is the mass of the photo frame?