Scientific Measurement

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Measurement in Agriculture

It is important to be honest when reporting a measurement, so that it does not appear to be more accurate than the equipment used to make the measurement allows. We can achieve this by controlling the number of digits, or significant figures, used to report the measurement

Significant figures are important because they tell us how good the data is. 100 grams 100. grams 100.00 grams

Significant Figures Rules:   Significant figures in a measurement include all of the digits that are known precisely plus one last digit that is estimated. 1. Non-zero digits are always significant. 103.230002 2. All final zeros after the decimal point are significant. 12.740 ; 0.0420 3. Zeros between two other significant digits are always significant. 10.0 ; 2004 ; 6.000 4. Zeros used only for spacing the decimal point are NOT significant. 100 ; .00000233

Examples of Sig Figs Given .00357 only 357 are important. Given 65,000 only 65 is important. Given 21,000.0078 all numbers are significant.

Practice! 1) 5.40 ____ 6) 1.2 x 103 ____ 2) 210 ____ 7) 0.00120 ____ 2) 210 ____ 7) 0.00120 ____   3) 801.5 ____ 8) 0.0102 ____ 4) 1,000 ____ 9) 9.010 x 10-6 ____ 5) 101.0100 ____ 10) 2,370.0 ____

Scientific Notation In our effort to make really large and really small numbers workable, we use scientific notation. In scientific notation, a number is written as a product of two numbers: a coefficient and a power of 10. Move the decimal so that the number is between 1 and 10 Example: If given, 36,000,000,000 we can use 3.6 X 1010 instead. Or, given .0000047 we can use 4.7 X 10 -6

Identify the number of sig figs Practice putting these numbers in scientific notation Keep the same number of sig figs! 1. 3,777,005 2. 100,000,000 3. 100,876 4. 0.77754003 5. 0.0000067 6. 0.0084 Identify the number of sig figs Put number in scientific notation while keeping the proper number of sig figs

Practice!! Worksheet in packet!

Addition, Subtraction, Multiplication, and Division Addition and Subtraction If you add or subtract, the answer is rounded to the same number of decimal places as the measurement with the least number of decimal places. 334.540 + 198.9916 = 0.0610 - 0.18 = Multiplication and Division If you multiply or divide two numbers, the answer is rounded off to the number of significant figures in the least precise term used in the calculation (i.e. the number with the fewest sig figs). 34/10.1 = 44 x 20 =

Practice!

Accuracy, Precision, and Error Accuracy and Precision Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. Precision is a measure of how close a series of measurements are to one another. To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

Accuracy, Precision, and Error

1. 334.540 grams + 198.9916 grams = ___________________ 2. 34 grams / 10.1 mL = ___________________ 3. 2.61 x 106 joules / 0.0034 seconds = ___________________  4. 0.0610 m – 0.18 m = ___________________   5. 349.0 cm + 1.10 cm + 100. cm = ___________________ 6. 252 meters / 910 seconds = ___________________ 7. 248.01010 kilograms + 84.097 kilograms = ___________________ 8. 44 m/s x 20 s = ___________________

Calculate the density of each of the following: 252 mL of a solution with a mass of 500. g   252 mL of a solution with a mass of 500 g    A 6.75 g solid with a volume of 5.35 cm3 50.0 mg of a gas which occupies a volume of 0.0064 L A substance with a mass of 7.55 x 104 kg and a volume of 9.50 x 103 L

Addition and Subtraction When adding or subtracting, the exponents must be made to be equal. In order to do this, the decimal point is moved, and the numbers with decimal points are added. The power of 10 stays the same. If, (5.4 x 104) + (6.0 x 102) then, 5.4 x 104 + 0.06 x 104 5.46 x 104 ! Round to 5.5 x 104

Multiplying and Dividing Ex: (3 x 104) X (2 x 102) 3 x 2 = 6 104+ 102= 106 So, 6 X 106 is the answer. (10 x 104 ) (2 x 102 ) 10 / 2 = 5 104 -102 = 102 5 x 102 is the answer. When multiplying in scientific notation, the coefficients are multiplied, and the exponents are added. When dividing in scientific notation, the coefficients are divided and the exponents are subtracted.

In a nut shell… Identify the number of sig figs If you want to put a number into scientific notation with the proper sig figs First ID the Sig Figs Ex: 0.000167 has 3 Sig Figs. (1,6,and7) Next these are then made to fit between 1-10. So, 0.000167 becomes 1.67 When we did this the decimal moved 4 spots to the right. The exponent reflects this move. (10-4) We get: 1.67 x 10-4 In a nut shell… Identify the number of sig figs Put number in scientific notation while keeping the proper number of sig figs

The six is then rounded up to 7. 43.657 has 5 Sig Figs Say we only want to have three significant figures, which are the 4,3,and 6. The six is then rounded up to 7. So 43.657 becomes 4.37 When we did this the decimal moved 1 spot to the left. The exponent reflects this move. (101) We get: 4.37 x 101