Unit 2

Unit 7Measurements in ChemistryScientific notation and Significant FiguresSCIENTIFIC NOTATIONWe commonly measure objects that are many times larger or smaller than our standard of comparisonWriting large numbers of zeros is tricky and confusingthe sunsdiameter is1,392,000,000 man atoms average diameter is0.000 000 000 3 mScientific notation expresses a number as the product of two factors: M x 10n 1 M 10 and n is an integerNumbers > one have a positive exponentNumbers < one have a negative exponent.Ex.120000 = 1.2 X 105 0.000054 = 54 x 10-4 (incorrect)0.000054 = 5.4 x10-5 (CORRECT)Writing a Number In Scientific Notation0.00012340Locate the Decimal Point0.00012340Move the decimal point to the right of the first non-zero digit from the left1.2340Multiply the new number by 10nwhere n is the number of places you moved the decimal pt.1.2340 x 104if the number is 1, n is +; if the number is < 1, n is -1.2340 x 10-404Writing a Number In Scientific Notation154000Locate the Decimal Point154000.Move the decimal point to the right of the first non-zero digit from the left1 . 54000 Multiply the new number by 10nwhere n is the number of places you moved the decimal pt.1 . 54 X 105if the number is 1, n is +; if the number is < 1, n is -05Writing a Number in Standard Form1.234 x 10-6since exponent is -6, make the number smaller by moving the decimal point to the left 6 placesif you run out of digits, add zeros000 001.2340.000 001 23406Change to scientific notation.

12,340 = 0.369 = 0.008 = 2,050,000,000 = Learning Check7Change to scientific notation.

12,340 = 0.369 = 0.008 = 2,050,000,000 = 1.234 x 1043.69 x 1018 x 1032.05 x 109Learning Check8Using the Exponent Keyon a CalculatorEXPEE

9EE or EXP means times 10 to theHow to type out 6.02 x 1023:6EE.03226y x.0322x16.02EE320y x32x16.020Dont do it like thisor like thisor like this:How to type out 6.02 x 1023:6EE.0322WRONG!WRONG!TOO MUCH WORK.10

Example:

1.2 x 1052.8 x 1013

But instead is written=1.2EE5

32.8EE1Type this calculation in like this:This is NOT written4.394.2857143 09Calculator gives4.2857143 E09or4.3 x 10911

Learning Check (we will learn how to round later)12

= -6.525 x 10-9= 5.3505 x 103 or 5350.5= 5.84178499 x 10-13= 2.904 x 1023

= -3.07122 x 1016Learning Check (we will learn how to round later)13Classwork: p 948 #1-3What is a Measurement?quantitative observationThey have a number and a unit (indicates what your are measuring Ex. m, s, C)

0Figure 2.29a

Accuracy and PrecisionAccuracy refers to how close the measured result is to the true valuePrecision refers to closeness to another series of measurement made on the same object- repeatabilitySIGNIFICANT FIGURES (DIGITS)Our measurements should reflect the precision of the instrument we used.

2.5 cm2.51 cmINCORRECT: 2.50154 cm Why? I cant read all this numbers with my instrument.The significant figures (sig figs) of a measurement are those digits known with certainty (read directly from the instrument) plus the last digit which is estimated.

2.34 cmCounting Significant Figures in MeasurementsAll nonzero digits are significant Ex. 725 cm has 3 sig. fig. 5.8 C has 2 sig. fig.

Zeros between nonzero digits are significant. Ex. 5.04s has 3 sig. fig. 7008 L has 4 sig. fig.

Zeros at the end of a number AND to the right of the decimal point are significant. Ex. 74.50 g has 4 sig figs 208.250 km has 6 sig figs 74, 000 hours has 2 sig figs 200 m has 1 sig fig

Zeros at the beginning of numbers are not significant.Ex. 0.0052mm has 2 sig fig 0.00000007800 g has 4 sig. fig. Counted values (18 students) and numbers in defined relationships (1m=100cm) have unlimited number of significant figures and never affect the number of significant figures in the results of a calculation.

Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation Ex. if 150m has 2 sig. figs. then 1.5 x 102 m

A decimal point is written intentionally to indicate the zero is significant.Ex. 150.m has 3 sig. figs.Learning Check: Determining the Number of Significant Figures in a NumberHow many sig figs are in each of the measurements?0.0035 m1.080 km2371 C 2.97 105 kg1 dozen = 12100,000 days100,000. days0Learning Check: Determining the Number of Significant Figures in a NumberHow many sig figs are in each of the measurements?0.0035 m2 sig figs1.080 km4 sig figs2371 C 4 sig figs2.97 105 kg3 sig. figs. only decimal parts count 1 dozen = 12unlimited100,000 days1 sig figs.100,000. days6 sig figs.0Rounding using Significant FiguresMultiplication and Division with Significant Figureswhen multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the fewest number of significant figures5.02m 89.665m 0.10m= 45.0118m3 = 45m33 sig. figs.5 sig. figs. 2 sig. figs. 2 sig. figs.

5.892 m 6.10s= 0.96590 m/s = 0.966 m/s 4 sig. figs. 3 sig. figs. 3 sig. figs.

0Roundingwhen rounding to the correct number of significant figures, if the number after the place of the last significant figure is 0 to 4, round down

5 to 9, round up0RoundingEx: round to 2 significant figures0.0234 rounds to 0.023 or 2.3 10-2because the 3 is where the last sig. fig. will be and the number after it is 4 or less0.0237 rounds to 0.024 or 2.4 10-2because the 3 is where the last sig. fig. will be and the number after it is 5 or greater0.0299865 rounds to 0.030 or 3.0 10-2because the 9 is where the last sig. fig. will be and the number after it is greater than 50Learning Check: Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result1.01 0.12 53.51 96 =56.55 0.920 34.2585 =0Learning Check: Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result1.01 0.12 53.51 96 = 0.06755656.55 0.920 34.2585 = 1.518630Determine the Correct Number of Sig. Figs. for each Calculation and Round the Result1.01 0.12 53.51 96 = 0.067556 = 0.06856.55 0.920 34.2585 = 1.51863 = 1.523 sf2 sf4 sf2 sfresult should have 2 sf 7 is in place of last sig. fig., number after is 5 or greater, so round up4 sf3 sf6 sfresult should have 3 sf 1 is in place of last sig. fig., number after is 5 or greater, so round up0Addition and Subtraction with Significant Figureswhen adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places5.74 + 0.823 +2.651= 9.214 = 9.21 2 dec. pl. 3 dec. pl. 3 dec. pl. 2 dec. pl.

4.8 - 3.965= 0.835 = 0.8 1 dec. pl 3 dec. pl. 1 dec. pl.

0Determine the Correct Number of Sig. Figs. for each Calculation and Round Result0.987 + 125.1 1.22 = 124.8670.764 3.449 5.98 = -8.6640Determine the Correct Number of Sig. Figs. And Round the Result0.987 + 125.1 1.22 = 124.867 = 124.90.764 3.449 5.98 = -8.664 = -8.663 dp1 dp2 dpresult should have 1 dp 8 is in place of last sig. fig., number after is 5 or greater, so round up3 dp3 dp2 dpresult should have 2 dp 6 is in place of last sig. fig., number after is 4 or less, so round down0Both Multiplication/Division and Addition/Subtraction with Sig. Figs.when doing different kinds of operations with measurements with significant figures, do whatever is in parentheses first, find the number of significant figures in the intermediate answer, then do the remaining steps3.489 (5.67 2.3) = 2 dp 1 dp3.489 3.37 =3.489 3.4 = 12 4 sf 2 sf 2 sf0Classwork: p951 #4 p953 #5-6