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Significant Figures

Rule #1 All non-zero digit numbers ARE significant Ex: 8.526 = 4 SD’s

Rule #2 Zeros between non-zero digit numbers ARE significant
Ex: 90,204 = 5 SD’s Ex: = 4 SD’s

Rule #3 All zeros to the left of the first non-zero number are NOT significant. Ex: = 2 SD’s Ex: 0.1 = 1 SD

Rule #4 When a number ends in zeros that are to the right of a decimal point, they ARE significant. Ex: = 3 SD’s Ex:3.0 = 2 SD’s Ex: = 2 SD’s (use Rule #3 also)

Rule #5 When a number ends in zeros that are not to the right of a decimal point, the numbers are not necessarily significant. Ex: 9,000,000,000 = 1 SD Ex: 50,100 = 3 SD’s Ex: 2,500 = 2 SD’s

Practice Problems 4 SD’s 5.432 = 0.189 = 2,873.0 = 3 SD’s 0.000235 =
2,500 = 1.04 X 1014 = = 7.500 X 108 = 1.000 X 103 = = 3 SD’s 5 SD’s 3 SD’s 2 SD’s 3 SD’s 4 SD’s 4 SD’s 4 SD’s 8 SD’s

Sig Fig Quick Quiz 3 SD’s 8.89 = 0.16 = 2,500.0 = 2 SD’s 0.00067345 =
36,700 = 6.093 X 1019 = = X 1024 = X 103 = = 2 SD’s 5 SD’s 5 SD’s 3 SD’s 4 SD’s 2 SD’s 5 SD’s 6 SD’s 10 SD’s

Sig Figs in Math Multiplying and Dividing 12.257m X 1.162m (5 SD)
Which number is smaller 5 or 4? 4 is smaller than 5 therefore you only want 4 SD in your answer! (5 SD) (4 SD) 14.24m2 (4 SD’s)

Sig Figs in Math Adding and Subtracting 3.95 g 2.879 g (2 SDAD)
Look AFTER the DECIMAL ONLY Adding and Subtracting 3.95 g 2.879 g g g Same as multiplication and division. Choose the smallest number for the answer. (2 SDAD) (3 SDAD) (1SDAD) 220.4 g (1 SDAD)

Sig Fig Math Problems 0.1273 mL – 0.000008 mL=
(12.4 cm X cm) cm2 ( g / 26 L) – g/L= = 0.1 mL (4 SDAD) (Only want 1 SDAD) (1 SDAD) (3 SD) (4 SD) cm2 = 98.5 cm2 cm2 = = 98.5 cm2 (2 SDAD) Only want 3 SD (1 SDAD) (Only want 1 SDAD) (5 SD) (2 SD) = 9.5 g/L g/L = 8.151 g/L = 8.2 g/L Only want 2 SD (1 SDAD) (3 SDAD) (Only want 1 SDAD)

Sig Fig Math Practice Problems
0.8102m X 3.44m= 94.20g / mL= 32.897g g= 34.09L – 1.230L= 2.79m2 (4 SD) (3 SD) 29.74g/mL (4 SD) (6 SD) 47.1g (3 SDAD) (1 SDAD) 32.86L (2 SDAD) (3 SDAD)

Sig Fig Sample Problem A (Pg. 59)
A student heats g of a solid and observes that its temperature increases from 21.6 °C to °C. Calculate the temperature increase per gram of solid. Gather Information Mass of Solid = g Initial Temp = 21.6 °C Final Temp = °C Plan Work A. Calculate temp. increase (Final temp – Initial temp) = temp increase B. Per gram of solid temp increase = temp increase per g of solid gram Calculate A. (36.79 °C – 21.6 °C ) = °C = B °C = = 23.62 g 15.2 °C 0.644 °C/g

Sig Fig Problem Practice
Do Pg 59 Practice Problems 1 & 2

Practice Problem #1 (Pg. 59)
Perform the following calculations, and express the answers with the correct number of significant figures. mL – mL = (12.4 cm X cm) cm2 = ( g / 26) – g = = 0.1 mL 4 SDAD 1 SDAD 3 SD 4 SD cm2 = 98.5 cm cm2 = = 1 SDAD 2 SDAD 98.5 cm2 5 SD 2 SD g = 9.5 g – g = 8.151 g = 8.2 g 1 SDAD 3 SDAD

Practice Problem #2 (Pg. 59)
A student measures the mass of a beaker filled with corn oil to be g. The mass of the beaker is g. Calculate the density of the corn oil if its volume is 114 cm3. Gather Info A. Mass of beaker + oil = g B. Mass of empty beaker = g C. Volume of corn oil = 114 cm3 Plan Work Mass of oil = A – B = X Density of oil = X__ C Calculate Mass of oil = g – g = Density of oil = g__ = 114 cm3 1 SDAD 1 SDAD 105.2 g 4 SD 0.923 g/cm3 3 SD

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