Lesson 5: Significant Digits AKA Significant Figures
First, take HW out to be checked. Keep it out. In CJ, copy down info from board. Keep CJ open to today s date at the top corner of your desk. On your Do Now sheet, copy and answer the questions/pictures below. 1. Length of line: 2. How many estimated digits should you record? 3. Draw a line that is 1.42 cm. (draw the ruler too)
TEST #1 COMING UP 6S, 6O = Friday Oct. 12 th 6Ga, 6I = Monday Oct. 15 th Multiple choice. Cumulative. Bring your own calculator. I will not provide you one during the test.
Lesson 5: Significant Digits AKA Significant Figures
Measurement The in last digit measurements (underlined) is an estimate because the liquid level falls in between the lines.
Measurement Numbers from a measurement are. never exact values They always have some uncertainty due to the limitations of the measuring device and the skill level of the person taking the measurement.
Different tools have different degrees of. Measurements should always have all the digits that are known plus one estimated digit. precision
Volumetric Flask 1000 ml +/- 0.30 ml Erlenmeyer Flask 1000 ml +/- 5% Each tool will tell you the measure of precision.
4.31 cm 3.5 cm Pink digit is estimated 5 cm Top one Lines correspond to smallest length increments Which ruler is most precise? Why? The number of digits in each measurement correspond to the precision of the instrument.
Q: What are Significant Digits? A: Digits that carry meaning contributing to the and of the measurement precision accuracy The number of significant figures in an expression indicates the confidence or precision with which an engineer or scientist states a quantity.
It s important to be honest when reporting a measurement, so that your measurement does not appear to be more accurate than the equipment used to make the measurement allows.
Too many estimated digits Correct Line isn t that close to 5 cm
Mike: 3.97 cm Correct Incorrect. Reason: Correct Andy: 4 cm Correct Incorrect. Reason: Rounded up, not enough digits Vanessa: 3.89 cm Correct Incorrect. Reason: Line is longer than 3.9 cm Michele: 3.9 cm Correct Incorrect. Reason: Did not include an estimated digit
Q: How do we count the number of significant digits in a measurement? number of digits that are known plus one estimated digit A: It s the are considered significant in a measured quantity
First, take HW out to be checked. Keep it out. In CJ, copy down info from board. Keep CJ open to today s date at the top corner of your desk. On your Do Now sheet, copy and answer the questions/pictures below. 1. Length of line? 2. A number that is very accurate and precise has more / less significant digits than a number that is not as accurate or precise. 3. 1.00 g is more / less precise than 1 g.
Significant Digits RULES Non zero digits. All non-zero digits are significant Exact numbers. Exact numbers have an infinite number of significant digits. Includes: counting numbers (counting a number of definite things) and defined numbers (example: 100 cm = 1 m). There is no uncertainty with these numbers.
Significant Digits RULES SIGNIFICANT ZEROS between nonzero digits 205 ml = significant digits 2.08 g = significant digits 84.05 L = significant digits 12.008 = significant digits at the end of a number that has a decimal point 0.500 s = significant digits 28.120 mg = significant digits 4.00 ml = significant digits 30. g = significant digits
Significant Digits RULES SIGNIFICANT ZEROS between nonzero digits 205 ml = 3 significant digits 2.08 g = _3 significant digits 84.05 L = 4 significant digits 12.008 = 5 significant digits at the end of a number that has a decimal point 0.500 s = 3 significant digits 28.120 mg = 5 significant digits 4.00 ml = 3 significant digits 30. g = _2 significant digits
Significant Digits RULES NON-SIGNIFICANT ZEROS before the first nonzero digit 0.00082 mg = significant digits 0.0117 dl = significant digits at the end of a number without a decimal point 2000 L = significant digit 840 K = significant digits
Significant Digits RULES NON-SIGNIFICANT ZEROS before the first nonzero digit 0.00082 mg = 2 significant digits 0.0117 dl = 3 significant digits at the end of a number without a decimal point 2000 L = 1 significant digit 840 K = 2 significant digits
Q: Are non-significant zeros still important? YES! A: These are placeholder zeros and they indicate where the decimal point belongs.
Sig. Digits: 1 2 3 4
Rounding with Significant Digits When using calculators, we often obtain numbers that have too many digits than are. We must round and drop the excess digits to properly and fairly express measurements. reasonable
4 or less? round down and stay the same 5 or more? round up
Multiplication & Division The answer must contain the same number of significant digits as the measurement that has the least number of significant digits.
Additional Vocabulary The more significant digits a measurement has, the more accurate and precise it is. Your measurement should accurately reflect the accuracy and precision of your instrument. Accuracy: how close a measurement is to the correct value for that measurement Precision: refers to how close two or more measurements are to each other, regardless of whether those measurements are accurate or not. A precise measuring tool is one that can measure values in very small increments.