Measurements in Chemistry Scientific notation and Significant Figures

SCIENTIFIC NOTATION We commonly measure objects that are many times larger or smaller than our standard of comparison Writing large numbers of zeros is tricky and confusing the sun’s diameter is 1,392,000,000 m an atom’s average diameter is m

Scientific notation expresses a number as the product of two factors: M x 10 n 1 ≤ M  10 and n is an integer Numbers > one have a positive exponent Numbers < one have a negative exponent. Ex = 1.2 X = 54 x (incorrect) = 5.4 x10 -5 (CORRECT)

Writing a Number In Scientific Notation Locate the Decimal Point Move the decimal point to the right of the first non-zero digit from the left Multiply the new number by 10 n where n is the number of places you moved the decimal pt x if the number is  1, n is +; if the number is < 1, n is x 10 -4

Writing a Number In Scientific Notation Locate the Decimal Point Move the decimal point to the right of the first non- zero digit from the left Multiply the new number by 10 n where n is the number of places you moved the decimal pt X 10 5 if the number is  1, n is +; if the number is < 1, n is -

Writing a Number in Standard Form x since exponent is -6, make the number smaller by moving the decimal point to the left 6 places if you run out of digits, add zeros

Change to scientific notation. 12,340 = = = 2,050,000,000 = Learning Check

Change to scientific notation. 12,340 = = = 2,050,000,000 = x x 10 –1 8 x 10 – x 10 9 Learning Check

Using the Exponent Key on a Calculator EXPEE

EE or EXP means “times 10 to the…” How to type out 6.02 x : 6EE y x x EE320y x 32 x Don’t do it like this… …or like this… …or like this: How to type out 6.02 x : 6EE WRONG! TOO MUCH WORK.

Example: 1.2 x x But instead is written… = 1. 2EE Type this calculation in like this: This is NOT written…4.3 – –09 Calculator gives… E–09 or… 4.3 x 10 –9

Learning Check (we will learn how to round later)

= x = x 10 3 or = x = x = x 10 16

Classwork: p 948 #1-3

What is a Measurement? quantitative observation They have a number and a unit (indicates what your are measuring Ex. m, s,  C)

Figure 2.29a Accuracy and Precision -Accuracy refers to how close the measured result is to the true value -Precision refers to closeness to another series of measurement made on the same object- repeatability

SIGNIFICANT FIGURES (DIGITS) Our measurements should reflect the precision of the instrument we used. 2.5 cm 2.51 cm INCORRECT: cm Why? I can’t 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 cm

Counting Significant Figures in Measurements 1. All nonzero digits are significant Ex. 725 cm has 3 sig. fig. 5.8  C has 2 sig. fig. 2. Zeros between nonzero digits are significant. Ex. 5.04s has 3 sig. fig L has 4 sig. fig.

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

4. Zeros at the beginning of numbers are not significant. Ex mm has 2 sig fig g has 4 sig. fig. 5. 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 10 2 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 Number How many sig figs are in each of the measurements? m km 2371  C 2.97 × 10 5 kg 1 dozen = ,000 days 100,000. days

Learning Check: Determining the Number of Significant Figures in a Number How many sig figs are in each of the measurements? m2 sig figs km4 sig figs 2371  C 4 sig figs 2.97 × 10 5 kg 3 sig. figs. – only decimal parts count 1 dozen = 12unlimited 100,000 days1 sig figs. 100,000. days6 sig figs.

Rounding using Significant Figures

Multiplication and Division with Significant Figures when 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 figures 5.02m × m × 0.10m= m 3 = 45m 3 3 sig. figs.5 sig. figs. 2 sig. figs. 2 sig. figs m ÷ 6.10s= m/s = m/s 4 sig. figs. 3 sig. figs. 3 sig. figs.

Rounding when rounding to the correct number of significant figures, if the number after the place of the last significant figure is 1. 0 to 4, round down 2. 5 to 9, round up

Rounding Ex: round to 2 significant figures rounds to or 2.3 × because the 3 is where the last sig. fig. will be and the number after it is 4 or less rounds to or 2.4 × because the 3 is where the last sig. fig. will be and the number after it is 5 or greater rounds to or 3.0 × because the 9 is where the last sig. fig. will be and the number after it is greater than 5

Learning Check: Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result × 0.12 × ÷ 96 = × ÷ =

Learning Check: Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result × 0.12 × ÷ 96 = × ÷ =

Determine the Correct Number of Sig. Figs. for each Calculation and Round the Result × 0.12 × ÷ 96 = = × ÷ = = sf2 sf4 sf2 sf result should have 2 sf 7 is in place of last sig. fig., number after is 5 or greater, so round up 4 sf 3 sf6 sf result should have 3 sf 1 is in place of last sig. fig., number after is 5 or greater, so round up

Addition and Subtraction with Significant Figures when 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 places = = dec. pl. 3 dec. pl. 3 dec. pl. 2 dec. pl = = dec. pl 3 dec. pl. 1 dec. pl.

Determine the Correct Number of Sig. Figs. for each Calculation and Round Result – 1.22 = – – 5.98 =

Determine the Correct Number of Sig. Figs. And Round the Result – 1.22 = = – – 5.98 = = dp1 dp2 dp result should have 1 dp 8 is in place of last sig. fig., number after is 5 or greater, so round up 3 dp 2 dp result should have 2 dp 6 is in place of last sig. fig., number after is 4 or less, so round down

Both 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 steps × (5.67 – 2.3) = 2 dp 1 dp × 3.37 = × 3.4 = 12 4 sf 2 sf 2 sf

Classwork: p951 #4 p953 #5-6