Set up clickers Significant Figures Finish up measurement lab Go over homework/quizzes Scientific Notation Practice Problems Homework tonight will be to complete the practice problems. They are posted on the class website. Navigate to our class section and download the word document. If anyone would like a hard copy, let me know. Slides saved as Sig Fig Sci Notation 2

Precision vs. Accuracy Example: a 100-meter dash is timed by four different judges. Here are the results: Judge s Judge 29.6 s Judge s Judge 410 s Which is the most precise measurement? Which is the least accurate? Judge 1 Judge 3

Precision vs. Accuracy Judge s Judge 29.6 s Judge s Judge 410 s Accuracy is how close the measurement is to the actual value. Because Judge 3 had a time that was significantly different than the others, we can assume that her time was inaccurate. Precision is a gauge of how exact a measurement is. Therefore, the most precise measurement was taken by Judge 1.

Significant Figures

What is the point of Significant Figures (sig figs) Different measuring tools offer different precision When using measurements in mathematical calculations, you can only report the precision of the least precise calculation that goes into the measurement. That is what sig figs is all about – reporting the best answer possible and rounding off the answer where appropriate.

…so which digits are considered significant? 1.All non-zero digits are significant 203.0, 0.404, 1000, , 0.404, 1000, Zeros between significant figures are significant 203.0, 0.404, 1000, All final zeros after the decimal point are significant 203.0, 0.404, 1000, Zeros only used for spacing are not significant 203.0, 0.404, 1000, 11.00

If you see a number containing zeroes with a decimal point at the end, that decimal point means that these zeroes are significant cm 7,700. mL 100,000,000. K

How many sig figs? ,

Rounding rules for addition and subtraction If you add or subtract, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places m 6.50 m 5.3 m 5.3 m +3 m +3 m m m 15 m is the answer you should report 15 m is the answer you should report 2 decimal places 1 decimal place 0 decimal places

Addition example For example, let’s say you want to find the total mass of 3 fish. Their masses are 12.1g, 11.23g, and g g 12.1 g g g g g g Answer to report is 37.4 g You cannot report your answer to the thousandths place because of the fact that your least precise measurement only goes to the tenths place!

sig fig rules for multiplication and division If you multiply or divide two numbers, the answer is rounded off to the number of significant figures in the measurement with the least number of sig figs g / 6.00 g = g 5 sig figs The reported answer should be 2.00 g because it has 3 sig figs 3 sig figs

Division example Lets say you wanted to determine the density of an object that had a mass of 2.2 kg and a volume of 3.3 cm 3 density = mass/volume = 2.2 kg 3.3 cm cm 3 = kg/cm 3 = 0.67 kg/cm 3

Scientific Notation

Mass of the Earth 5,970,000,000,000,000,000,000,000 kg Almost six septillion kilograms

Radius of a carbon atom m 70 trillionths of a meter

Scientific Notation Used to write numbers that are very large or very small so that they can be easily understood and used for calculations Used to write numbers that are very large or very small so that they can be easily understood and used for calculations Conveys the number of significant digits and order of magnitude Conveys the number of significant digits and order of magnitude

Ever see “E” on a calculator? E means “times ten to the” 5.124E12 =5.124 x m

Significant figures and scientific notation The rules are the same for the number that comes before the multiplier x atoms 4 sig figs 4 sig figs

You can use scientific notation to report your answer in the appropriate number of sig figs 1500 cm x 15 cm = 22,500 cm cm x 15 cm = 22,500 cm 2 2 sig figs 2 sig figs 2 sig figs 2 sig figs your reported answer can only have two sig figs, therefore it could be 23,000 cm 2 or 2.3 x 10 4 cm 2

Sometimes you need scientific notation to express the correct number of significant figures Calculate the area of a factory with a length of 340 m and a width of 29.5 m. (340m)(29.5m) = 10300m. You need 2 significant figures. How can you write 10300m with 2 sig figs? 1.0 x 10 4 m

Significant figures in scientific notation An electron's mass is about kg. An electron's mass is about kg. In scientific notation, this is written ×10 − 31 kg. In scientific notation, this is written ×10 − 31 kg. Note that all the zeros before the 9 are not significant. Note that all the zeros before the 9 are not significant.

Adding and subtracting with Scientific Notation You can only add and subtract in scientific notation if the exponents are the same If the exponents are the same, you just add or subtract the numbers and leave the exponent alone Here is an example: = 6000 In scientific notation 4000 = 4 x 10 3 and 2000 = 2 x 10 3 (4 x 10 3 ) + (2 x 10 3 ) = 6 x 10 3 Note that the numbers were added, but the exponents remained the same

Adding and subtracting with Scientific Notation If you have two numbers in scientific notation, you have to make the exponents the same before you can add or subtract Here is an example: 10,000 – 5,000 = 5,000 (1 x 10 4 ) – (5 x 10 3 ) You need to change one of them so that their exponents are equal! (10 x 10 3 ) – (5 x 10 3 ) = 5 x 10 3

Multiplying with scientific notation When you multiply in scientific notation, you multiply the numbers and then add the exponents. When you multiply in scientific notation, you multiply the numbers and then add the exponents. (3.2 x 10 7 )(1.0 x ) = 3.2 x (3.2 x 10 7 )(1.0 x ) = 3.2 x (2.5 x )(2.00 x ) = (2.5 x )(2.00 x ) = 5.0 x 10 8

Dividing with Scientific Notation When you divide in scientific notation, you divide the numbers and then subtract the exponents. Here is an example: 6.2 x = 2.0 x x x x = ??? 3.00 x 10 5 = 3.0 x

Practice Problems! 1.find the total mass of 20.2 kg and kg 2.find the area of a rectangle that has a length of 10.0 m and a width of m (a=l x w) 3.find the change in mass of a 2.00 kg piece of dry ice that lost 0.50 kg 4.find the change in mass of a 4.00 kg piece of dry ice that lost 0.5 kg 5.find the density of a sample of water that has a mass of g and a volume of cm 3 (d=m/v) 6.find the total volume of 2 objects that are 2.33 x 10 3 L and 1.0 x 10 2 L

More Practice! 7.multiply 3.05 x km and x 10 5 km 8.divide 6.00 x m by 3.0 x 10 5 m sec/ m 10. (6.6 x ) (3.30 x ) /200

More practice! Put the following numbers in scientific notation with the appropriate number of sig figs! , , ,000,000,