ACCURACY AND PRECISION

TRUE VALUE – quantity used 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

(or how many numbers should I report?) SIGNIFICANT FIGURES (or how many numbers should I report?)

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

NUMBER OF SIGNIFICANT FIGURES EXAMPLES NUMBER OF SIGNIFICANT FIGURES COMMENT 453 kg 3 All non-zero digits are always significant. 5057 L 4 Zeros between 2 significant figures are significant. (SANDWICH RULE) 5.00 cm For the zero on the rightmost position, zeroes to the right of the decimal point are significant. Zeroes in between significant figures are significant. 500 s 1 Placeholders are not significant

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

PERCENTAGE ERROR Example : Actual value = 100.0 Obtained using the following steps: Determine the absolute value of the difference between the actual value and the measured value. Divide the difference by the actual value. Multiply by 100 % to obtain percentage error. Example : Actual value = 100.0 Measured value is 101.2 % Error = /Actual value-measured value/ x 100% actual value = / 100.0 – 101.2 / X 100% = 1.20 % 100

INTERNATIONAL SYSTEM (SI) OF MEASURE

SI BASE UNITS QUANTITY UNIT SYMBOL Length meter m Mass kilogram kg Time second s Amount of substance mole mol Current ampere A Temperature kelvin K Luminous intensity candela cd

NUMERICAL PREFIXES FACTOR PREFIX SYMBOL 10 18 exa E 10 -1 deci d 10 15 peta P 10 -2 centi c 10 12 tera T 10 -3 milli m 10 9 giga G 10 -6 micro u 10 6 mega M 10 -9 nano n 10 3 kilo k 10 -12 pico p 10 2 hecto h 10 -15 femto f 10 1 deka da 10 -18 atto a

CONVERSION OF UNITS (Ex) 100 m = ___________ mm 100 m = (100 m) (10 dm) (10cm) (10 mm ) 1m dm cm = 100 000 mm

FORMULA TRANSFORMATION Given the formula: 3A + B = Z, solve for A 3A + B = Z 3A = Z - B A = Z-B 3 -B -B 3 3

IMPORTANCE OF FORMULA TRANSFORMATION