 Scientific Notation Converting into Sci. Notation: –Move decimal until there’s 1 digit to its left. Places moved = exponent. –Large # (>1)  positive.

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Scientific Notation Converting into Sci. Notation: –Move decimal until there’s 1 digit to its left. Places moved = exponent. –Large # (>1)  positive exponent Small # (<1)  negative exponent –Only include sig figs. 65,000 kg  6.5 × 10 4 kg

Scientific Notation 1. 2,400,000  g 2. 0.00256 kg 3.7  10 -5 km 4. 6.2  10 4 mm Practice Problems 2.4  10 6  g 2.56  10 -3 kg 0.00007 km 62,000 mm

Calculating with Scientific Notation Example: (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE 78.1 4 = 671.6049383= 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator:

Accuracy and Precision Percent Error Significant Figures Chemistry Math

A. Accuracy vs. Precision Accuracy – a measure of how close a measurement comes to the true value Precision – a measure of how close a series of measurements are to one another. ACCURATE = CORRECT PRECISE = CONSISTENT

Example: Low accuracy – high precision High accuracy – low precision High accuracy – high precision

B. Calculating Percent Error Error – the difference between the experimental value and the accepted value. your value true value

B. Percent Error A student determines the density of a substance to be 1.40 g/mL. Find the error and the % error if the accepted value of the density is 1.36 g/mL.

SIGNIFICANT FIGURES A New Way To Count Numbers

C. Significant Figures Indicates the precision of a measurement. Recording Sig Figs –Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

2.83 cm 4.50 cm 15.0 o C28.5 o C30.0 mL4.29 mL

C. Significant Figures Counting Sig Figs –Count all numbers EXCEPT: »Leading zeros -- 0.0025 »Trailing zeros without a decimal point -- 2,500

4. 0.080 3. 5,280 2. 402 1. 23.50 C. Significant Figures Counting Sig Fig Examples 1. 23.50 2. 402 3. 5,280 4. 0.080 4 sig figs 3 sig figs 2 sig figs

NON ZERO DIGITS A non zero digit is any number but zero 4, 6, 12, 7, 9, 1 are all non zero digits 1.48593 62.7

CAPTIVE ZEROS Captive zeros are those in between two numbers 604 1.007 60.4057

LEADING ZEROS Leading zeros are zeros at the beginning of the number. 0.0042 0.000008

TRAILING ZEROS Zeros that come at the end of a number 450 1.600 30.0 ZEROS

Scientific Notation All numbers in the first number are significant. 3.40 X 10 -5 6.02 x 10 23 9.64 x 10 -10

C. Significant Figures Calculating with Sig Figs –Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g  7.9 mL  350 g 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g

C. Significant Figures Calculating with Sig Figs –Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = 324.103g 324 g 4 SF3 SF

EXACT NUMBERS 1.Exact numbers have infinite number of significant figures. Exact numbers include 1.Counting of anything : 22 people or 10 meter sticks, 6 eggs etc. 2.Defined quantities : 12 = 1 doz. 2.Exact numbers do not affect the rounding to the correct number of significant figures or in the calculations of the measurements.

C. Significant Figures 1. (15.30 g) ÷ (6.4 mL) Practice Problems = 2.390625 g/mL  18.1 g 2. 18.9g - 0.84 g 18.06 g 4 SF2 SF  2.4 g/mL 2 SF

Practice Problems (pg. 70 &71). 3). 61.2 meters + 9.35 meters + 8.6 meters = 4). 8.3 meters x 2.22 meters= 5). 8.345 g / 10.6 mL =

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