Measurements Experiments are performed. Numerical values or data are obtained from these measurements.
12 inches = 1 foot100 centimeters = 1 meter Exact numbers have an infinite number of significant figures. Exact numbers occur in simple counting operations Exact Numbers Defined numbers are exact. 12345
Form of a Measurement 70.0 kilograms = 154 pounds numerical value unit
Significant Figures The number of digits that are known plus one estimated digit are considered significant in a measured quantity estimated 5.16143 known
Rounding Off Numbers Often when calculations are performed extra digits are present in the results. It is necessary to drop these extra digits so as to express the answer to the correct number of significant figures. When digits are dropped the value of the last digit retained is determined by a process known as rounding off numbers.
80.873 Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed. 4 or less Rounding Off Numbers
5 or greater 5.459672 Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1. drop these figures increase by 1 6 Rounding Off Numbers
In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.
(190.6)(2.3) = 438.38 438.38 Answer given by calculator. 2.3 has two significant figures. 190.6 has four significant figures. The answer should have two significant figures because 2.3 is the number with the fewest significant figures. Drop these three digits. Round off this digit to four. The correct answer is 440 or 4.4 x 10 2
602200000000000000000000 0.00000000000000000000625 Very large and very small numbers like these are awkward and difficult to work with. Very large and very small numbers are often encountered in science.
602200000000000000000000 A method for representing these numbers in a simpler form is called scientific notation. 0.00000000000000000000625 6.022 x 10 23 6.25 x 10 -21
Scientific Notation Write a number as a power of 10 Move the decimal point in the original number so that it is located after the first nonzero digit. Follow the new number by a multiplication sign and 10 with an exponent (power). The exponent is equal to the number of places that the decimal point was shifted.