Significant Figures and Scientific Notation Making Sense of BIG Numbers

What should an eagle be able to do? Accurately count the total number of significant digits Convert Scientific Notation to Numbers Convert Numbers to Scientific Notation Use Scientific Notation Mathematical rules for: Adding & Subtracting Dividing and Multiplying

Significant Numbers Rules made simple Numbers 1 – 9 are always significant. Zero Rules: 0.000222 Leading zeros 2000.00 Trailing zeros with decimal 2000 Trailing zeros without decimal 200002 Captive zeros

How to Convert Numbers to Scientific Notation If a number is greater than one, its exponent should be positive. Locate the original decimal place and move the decimal to the left until you get the right side of the 1st sig fig. For example: 203 ---> 2.03 x 102 2. If a number is less than one, Its exponent should be negative. right until you get the right side of the 1st sig fig. For example: 0.003 ---> 3 x 10-3

How to convert scientific notation to numbers If the exponent is positive, it means that the original number was greater than one. Move the decimal to the right For example: 23 x 10 1  230 If the exponent is negative, it means that the original number was less than one. Move the decimal to the left For example: 23 x 10-4  .0023

Mathematical rules for scientific notation Addition and subtraction (decimal places) FOR EXAMPLE Count the # of decimal places to determine the number of significant figures. The answer cannot contain more places after the decimal point than the smallest number of decimal places in the numbers being added or subtracted. 23.112233 (6 places after decimal) 1.3324 ( 4 places after decimal) + 0.25_ ( 2 places after decimal) Since 0.25 has the least # of decimal places, your answer should have 2 places after the decimal point On calculator you get  24.694633 Your final answer should be  24.69

Mathematical rules for scientific notation Multiplication and division (Sig FiGs) For Example Count the # of significant figures. The answer cannot contain more significant figures than the number being multiplied or divided with the least number of significant figures. 23.123123 (8 sig figs) X 1.3344 (5 sig figs) Since 1.3344 has the least # of sig figs then your answer should have 5 sig figs On your calculator you get: 30.855495 Your final answer should be: 30. 855

It’s now Time to practice! PowerPoint Courtesy of Ms. Christal Owens 2011 WHS Chemistry Team