Mastery of Significant Figures, Scientific Notation and Calculations Goal: Students will demonstrate success in identifying the number of significant figures within a number, converting decimal form to scientific notation and calculating and rounding an answer properly Chemistry

SIGNIFICANT FIGURES All non-zero digits are significant. 825 has three sig. fig. Zeros located between non-zero digits are significant has four sig. fig. When a decimal or mixed decimal ends in zero, the zero is significant has five sig. fig. When a whole number ends in zero (with no decimal point), the zero is not significant. 400 has one sig. fig. When a whole number ends in zero (with a decimal point), the zero is significant 450. has three sig. fig.

Identifying Significant Figures , ,000,000,

More Converting , ,000,000,

More Converting = x ,000 = 9.5 x = x = 1.01 x = x = 1.0 x = x = 4.00 x = 1 x ,000,000, = 5.20… x 10 10

More Identifying ,000,000,000,000,000,000, x ,010,101,000 52,

Converting Scientific Notation ,000,000,000,000,000,000, x ,010,101,000 52,

Converting Scientific Notation = 2.00 x ,000,000,000,000,000,000,000 = 6.02 x x10 8 = 3.00 x = 2.00 x = 2.5 x = 5 x = x ,010,101,000 = x ,000.0 = x = x 10 1

Converting from Sci. Not. To Decimal x x x x x x x x x 10 -6

Converting from Sci. Not. To Decimal x , x x x ,010, x x x x x

Addition Subtraction Rules for Sig. Figs. Adding and Subtracting: Add or Subtract using your calculator, and round the answer to the least accurate decimal place = => 17.9 the tenths place in 0.1 is the least accurate decimal place.

+/- with Sig Figs = = – = , = – 79.5 =

+/- with Sig Figs =  =  – =  , =  – 79.5 =  984.6

More +/- with sig figs = – 8.23 = = – – = – =

More +/- with sig figs =  – 8.23 =  =  – – =  – =  8.02

Multiplication and Division with Sig. Figs. Round off to the least number of significant figures in any individual factor. i.e. (25.1) (3.9) (0.0016) = => The answer must be rounded to 2 sig. figs.

Multiply/Divide with Sig. Figs 1.(0.102) (0.0821) ( 273) / (1.01) = 2.(0.14) (6.022 X )= 3.(4.0 X 10 4 ) ( ) ( ) = 4.(2.00 X 10 6 ) / (3.00 X ) = 5.( ) (25,000) / (52.01) =

Multiply/Divide with Sig. Figs 1.(0.102) (0.0821) ( 273) / (1.01) =  (0.14) (6.022 X )= X  8.4 X (4.0 X 10 4 ) ( ) ( ) = 153,  150,000 4.(2.00 X 10 6 ) / (3.00 X ) = X  6.67 X ( ) (25,000) / (52.01) =  2.5

More Multiply Divide 6.(2.50) (0.0015) / (10.) = 7.(200.0) (8.1) / (0.0010) = 8.(350) (5.001) / ( ) = 9.(5,000,000) (10.) / (1,000,000) =

More Multiply Divide 6.(2.50) (0.0015) / (10.) =  (200.0) (8.1) / (0.0010) = 162,000  160,000 8.(350) (5.001) / ( ) = 1,750,350  1,800,000 9.(5,000,000) (10.) / (1,000,000) =  50

CFA #1 Convert the following from decimal to scientific notation ,000 Calculate the following and use significant figure rules to round the answer properly = 5.(100.0) (1.000) (1.0) = 6. (100.) (1.000) / (10)=

CFA #1 Convert the following from decimal to scientific notation x x , x 10 5 Calculate the following and use significant figure rules to round the answer properly = (100.0) (1.000) (1.0) =1.0 x (100.) (1.000) / (10)=10