Measurements & Calculations Accuracy, Precision, % Error, Scientific Notation

Accuracy vs. Precision Accurate Precise The closeness of measurements to the correct or accepted value of quantity measured Precise The closeness of a set of measurements of the same quantity made in the same way Measured values that are accurate are close to the accepted value. Measured values that are precise are close to one another, but not necessarily close to the accepted value.

% Error There are a couple ways error could occur in your measurements: Human Error – mistakes in experiment, measurements, etc. Equipment Error – faulty or broken equipment, etc. Calculating Error Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100. Accepted Value – true/correct value (look it up!) Experiment Value – measured in the experiment Error = Accepted Value – Experimental Value Error = accepted value – experimental value – this can be positive or negative depending on what value is higher or lower. Units of error are the same as the measurements (grams, cL, etc.) Percentage error = (valueexperimental – value accepted) or error / valueaccepted x 100 = % error -- We always make it an absolute, or positive, value of error as a percentage. And % is our only unit “sign” for error. A student measures the mass and volume of a substance and calculates the density as 1.40g/ml. The correct, or accepted, value of density is 1.30g/ml. What is the percentage error of the students measurements? 1.40g/ml – 1.30 g/ml / 1.30 g/ml = 0.0769 x 100 = 7.7% What is the percentage error for a mass measurement of 17.7 grams, given that the correct value is 21.2 grams? 17.7 g – 21.2 g / 21.2g = 0.165 = -16.5%

Scientific Notation Numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10, and n is a whole number. Coefficient – the number greater than or equal to 1 but less than 10 Exponent – is the whole number that indicates how many times the coefficient must be multiplied by 10(+) or by 1/10(-) 65,000 km or 6.5 x 104 km 0.00012 mm or 1.2 x 10-4 mm Steps: Determining M by moving the decimal point in the original number to the left or the right so that only one nonzero digit remains to the left of the decimal point. Determine n by counting the number of places that you moved the decimal point. If you moved it to the left, n is positive. If you moved it to the right, n is negative. Change a large number by moving the decimal to the left – exponent will be a positive number. 564000000000 = 5.64 x1011 Change a small number by moving the decimal to the right – exponent will be a negative number. 0.000000087 = 8.7 x 10-8

Adding or Subtracting Scientific Notation These operations can only be performed when the values have the same exponents, or n factor. If they do not, adjustments must be made to the values so that the exponents are equal. M factors can be added or subtracted The exponents of the answer remain the same Or it may be adjusted to the M factor stays between 1 and 10 4.2 x 104 kg + 7.9 x 103 kg Adjust 7.9 x 103 to .79 x 104 . Add and come up with 4.99 x 104 kg or 5.0 x 104 kg OR Adjust 4.2 x 104 to 42 x 103. Add and come up with 49.9 x 103, kg. 4.99 x 104 kg, or 5.0 x 104 kg Same rules apply for subtraction. Try: 7.023 x 109 g – 6.62 x 107 g = 702.3 x 107 – 6.62 x 107 = 695.7 x 107 = 6.96 x 109

Multiplying & Dividing Scientific Notation Multiply coefficients and ADD exponents. (5.23 x 106 mm)(7.1 x 10-2 mm) (5.23 x 7.1) x 104 = 37.133 x 104 mm or 3.71 x 105 mm2 The coefficients are divided, and the exponent of the denominator is subtracted from that of the numerator. 5.44 x 107 g = 5.44 x 107-4 g/mol = 0.6716 x 103 g/mol 8.1 x 104 mol 8.1 or 6.7 x 102 g/mol Calculate (8.99 x 10-4 m) (3.57 x 104 m) = 32.1 x 10 m2 Calculate 2.17 x 10-3 g / 5.002 x 104 mL = 0.434 x 10-7 g/mL or 4.34 x 10-8 g/mL

Homework Measurement Review Worksheet Study for your Chapter 2 Test next class!!!