1	SIGNIFICANT FIGURES
2	RULES Significant Figure Rules Focus on these rules and learn them well. They will be used extensively throughout the remainder of this course. Please remember that, in science, all numbers are based upon measurements (except for a very few that are defined). Since all measurements are uncertain, we must only use those numbers that are meaningful. A common ruler cannot measure something to be 22.4072643 cm long. Not all of the digits have meaning (significance) and, therefore, should not be written down. In science, only the numbers that have significance (derived from measurement) are written.
3	PLAYING NAME THAT ZERO Rule 1: Non-zero digits are always significant. Hopefully, this rule seems rather obvious. If you measure something and the device you use (ruler, thermometer, triple-beam balance, etc.) returns a number to you, then you have made a measurement decision and that ACT of measuring gives significance to that particular numeral (or digit) in the overall value you obtain. Hence a number like 26.38 would have 4 sig fig 7.94 would have 3 sig fig’s. The problem comes with numbers like 0.00980 or 28.09.
4	CAPTURED ZERO’S Rule 2: Any zeros between two significant digits are significant. 408 has 3 significant figures
5	FINAL & TRAILING ZERO’S Rule 3: A trailing zeros in the decimal portion ONLY are significant. This rule causes the most difficulty with students. Here are two examples of this rule with the zeros this rule affects in boldface: 0.00500 3 sig fig’s 0.03040 4 sig fig’s Here are two more examples where the significant zeros are in boldface: 2.30 x 10 ^-53 sig fig’s 4.500 x 10¹²4 sig fig’s
6	FINAL ZERO’S to the LEFT of the DECIMAL POINT Rule 3: A FINAL zero to the LEFT of the decimal portion are NOT significant. This rule is broken when a line is placed over the zero’s like the 3^rd example 500 1 sig fig’s 3040 3 sig fig’s 4000 4 sig fig’s
7	LEADING ZERO’S Rule 3: A LEADING zero in the decimal portion are NOT significant. Here are two examples of this rule with the zeros this rule affects in GREEN: 0.00500 3 sig fig’s 0.03040 4 sig fig’s
8	EXACT NUMBERS Exact numbers, such as the number of people in a room, have an infinite number of significant figures. Exact numbers are counting up how many of something are present, they are not measurements made with instruments.
9	EXACT EXAMPLES Another example of this are defined numbers, LIKE 1 foot = 12 inches. There are exactly 12 inches in one foot. Therefore, if a number is exact, it DOES NOT affect the accuracy of a calculation nor the precision of the expression. Some more examples: There are 100 years in a century. 2 molecules of hydrogen react with 1 molecule of oxygen to form 2 molecules of water. There are 500 sheets of paper in one ream.
10	SUMMARY NON-ZERO DIGITS ARE SIGNIFICANT 468 3 SIG’S CAPTURED ZERO’S ARE SIGNIFICANT 603 3 SIG’S TRAILING ZERO’S(TO THE RIGHT FO THE DECIMAL) ARE SIGNIFICANT 451.30 5 SIG’S FINAL ZERO’S (TO THE LEFT OF THE DECIMAL) ARE NOT SIGNIFICANT 5100 2 SIG’S LEADING ZERO’S (NUMBERS LESS THAN ONE) ARE NOT SIGNIFICANT 0.0034 2 SIG’S