2 Rules for Significant Digits 1. All non-zero numbers (1-9) are significant (meaning they count as sig figs)613 = 3 sig figs= 6 sig figs2. Zeros located between non-zero digits are ALWAYS significant (they count)5004 = 4 sig figs602 = 3 sig figs= 16 sig figs!
3 Rules for Significant Digits 3. Trailing zeros (those at the end) are significant only if the number contains a decimal point; otherwise they are insignificant (they don’t count)5.640 = 4 sig figs= 6 sig figs= ONLY 2 sig figs4. Placeholder Zeros at the beginning of a decimal number are not significant= 3 sig figs0.052 = 2 sig figs= ONLY 2 sig figs!
4 Limits of MeasurementSignificant figures are all the digits that are known in a measurement, plus the last digit that is estimated.The precision of a calculated answer is limited by the least precise measurement used in the calculation.
5 Addition & Subtraction: Limits of MeasurementAddition & Subtraction:The solution to the calculation is limited by the least precise measurement:=Limited to only one place past the decimalCorrect answer = 162.7
6 Multiplication & Division: Limits of MeasurementMultiplication & Division:The solution to the calculation is limited by the measurement with the least number of sig figs:40.9 x 7.2 =Limited to only 2 sig figs Round the numberCorrect Answer = 290240/6 = 40Limited to only 1 sig fig 40 only has 1 sig fig (no decimal)
7 Using Scientific Notation Why is scientific notation useful?Scientists often work with very large or very small numbers.Astronomers estimate there are 200,000,000,000 stars in our galaxy.The nucleus of an atom is about meters wide.These an be awkward numbers to fully write out and read.
8 Using Scientific Notation Scientific notation expresses a value in two parts:First part: a number between 1 and 10Second part: “10” raised to some powerExamples:105 = 10 x 10 x 10 x 10 x 10 = 100,00010-3 = 1/10 x 1/10 x 1/10 = 0.1 x 0.1 x 0.1 = 0.001The 2 parts are then multipliedExample: 5,430,000 = 5.43 x 106
9 Using Scientific Notation General Form is: A.BCD… x 10QNumbers GREATER that 1 have POSTIVE Q’s (exponents)Example: x 104 = 12,300Numbers LESS than 1 have NEGATIVE Q’s (exponents)Example: 7.6 x 10-5 =
10 Using Scientific Notation “Placeholder” zero’s are droppedPlaceholders are used between the last non-zero digit and the decimal (even if decimal is not shown)Examples:2,570 = 2.57 x 103583,000 = 5.83 x 10515,060 = x 104= 5.6 x 10-3= x 10-2
11 Standard to Scientific Notation Move the decimal to create a number between 1-10 (there should never be more than one number to the left of the decimal!)Drop any zeros after the last non-zero numberExample: 6,570 6.57Write the multiplication sign and “10” after the new numberExample: 6.57 x 10
12 Standard to Scientific Notation The number of spaces you moved the decimal from its original place to create the new number becomes the EXPONENTExample: 6.57 x 103If the original number was GREATER than 1 you are done (the exponent will remain positive). If the original number was LESS than 1 (a decimal number) then your exponent will be NEGAVTIVEExample: x 10-3
13 Scientific Notation to Standard Start with the EXPONENT x 105Number of spaces & directionPositive Exp – ending number greater than 1Negative Exp – ending number less than 1Move decimal the designated number of spaces 50903_.Fill in empty spaces with ZERO’s 509,030.