ACCURACY AND PRECISION

TRUE VALUE – quantity use by general agreement of the scientific community ACCURACY- closeness of the measurements to the true value of what is being measured PRECISION – closeness of the measurements to one another

ACCURATE AND PRECISE

NOT ACCURATE NOT PRECISE

PRECISE NOT ACCURATE

SIGNIFICANT FIGURES 4.6 cm 4.58 cm 3.0 cm NOT 3 cm All the numbers that you are sure of plus an estimated number 4.6 cm 4.58 cm 3.0 cm NOT 3 cm

RULES IN DETERMINING SIGNIFICANT FIGURES (sf) 1. All non-zero digits are significant. Ex. 432 – 3 sf 2238 – 4 sf 2. Zeroes in between significant figures are significant (SANDWICH RULE). Ex. 1001 – 4 sf 3 000 006 – 7 sf 3. Zeroes to the right of a significant figure and to the right of the decimal point are significant (DOUBLE RIGHT). Ex. 100 – 1 sf 100.0 – 4 sf 0.001 – 1 sf 10.000 001 0 – 9 sf

ADDITION AND SUBTRACTION OF SIGNIFICANT FIGURES The sum or difference of the numbers should have the same number of decimal places as the quantity with the lowest decimal places. 5.0 + 2.111 7.111 1.00 - 0.1 0.9 1 - 0.1 0.9 0.9 1 7.1

MULTIPLICATION AND DIVISION OF SIGNIFICANT FIGURES The product or quotient of the numbers should have the same number of significant figures as the quantity with the lowest number of significant figures. 3 sf 2 sf 1.11 X 1 3 sf 1 sf 1.11 X 1.0 5.5 ÷ 1 2 sf 1 sf 1.1 2 sf 6 1 sf 1 1 sf

5.67 x 105 coefficient base exponent SCIENTIFIC NOTATION - method of expressing very large or very small numbers. It is a short hand method for writing numbers, and an easy method for calculations and is made up of three parts: the coefficient, the base and the exponent.  5.67 x 105         coefficient   base   exponent

In order for a number to be in correct scientific notation, the following conditions must be true: 1. The coefficient must be greater than or equal to 1 and less than 10. 2. The base must be 10. 3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation.  A negative exponent means that the decimal is moved to the left when changing to standard notation.

Ex.1 Change 6.03 x 107 to standard notation. Remember,  107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10 000 000 so,    6.03 x 107 = 6.03 x 10 000 000 = 60 300 000 answer = 60 300 000 Instead of finding the value of the base, we can simply move the decimal seven places to the right because the exponent is 7. So, 6.03 x 107 = 60 300 000

Ex.2 Change 5.3 x 10-4 to standard notation. The exponent tells us to move the decimal four places to the left. so, 5.3 x 10-4 = 0.0 0 0 5 3

Ex.3 Change 56 760 000 000 to scientific notation Remember, the decimal is at the end of the final zero. The decimal must be moved behind the five to ensure that the coefficient is less than 10, but greater than or equal to one. The coefficient will then read 5.676 The decimal will move 10 places to the left, making the exponent equal to 10. Answer equals 5.676 x 1010

Ex.4 Change 0.000000902 to scientific notation The decimal must be moved behind the 9 to ensure a proper coefficient. The coefficient will be 9.02 The decimal moves seven spaces to the right, making the exponent -7 Answer equals 9.02 x 10 -7