# SCIENTIFIC MEASUREMENT  CHEM IH: CHAPTER 3. What is Scientific Notation?  Scientific notation is a way of expressing really big numbers or really small.

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SCIENTIFIC MEASUREMENT  CHEM IH: CHAPTER 3

What is Scientific Notation?  Scientific notation is a way of expressing really big numbers or really small numbers.  For very large and very small numbers, scientific notation is more concise.

Scientific notation consists of two parts:  A number between 1 and 10  A power of 10 N x 10 x

Examples  Given: 289,800,000  Use: 2.898 (moved 8 places)  Answer: 2.898 x 10 8 (how many sig figs? Honors only)  Given: 0.000567  Use: 5.67 (moved 4 places)  Answer: 5.67 x 10 -4 (How many sig figs? Honors only)

Stating a Measurement In every measurement there is a  Number followed by a  Unit from a measuring device The number should also be as precise as the measuring device.

Ex: Reading a Meterstick. l 2.... I.... I 3....I.... I 4.. cm First digit (known)= 2 2.?? cm Second digit (known)= 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported=2.75 cm or2.74 cm or2.74 cm or2.76 cm

UNITS OF MEASUREMENT Use SI units — based on the metric system LengthMassVolumeTimeTemperature Meter, m Kilogram, kg Seconds, s Celsius degrees, ˚C kelvins, K Liter, L

Metric Prefixes

Significant Figures (Honors only) The numbers reported in a measurement are limited by the measuring tool The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit Significant figures in a measurement include the known digits plus one estimated digit

Counting Significant Figures: Non-Zero Digits (Honors Only) RULE 1. All non-zero digits in a measured number ARE significant. #of Significant Figures 38.15 cm4 5.6 ft2 65.6 lb___ 122.55 m 122.55 m___

Counting Significant Figures: Leading Zeros (Honors Only) RULE 2. Leading zeros in decimal numbers are NOT significant. #of Significant Figures 0.008 mm1 0.0156 oz3 0.0042 lb____ 0.000262 mL 0.000262 mL ____

Counting Significant Figures: Sandwiched Zeros (Honors Only) RULE 3. Zeros between nonzero numbers ARE significant. (They can not be rounded unless they are on an end of a number.) # of Significant Figures 50.8 mm3 2001 min4 0.702 lb____ 0.00405 m 0.00405 m ____

Counting Significant Figures: Zeros @ the End of a # & to the Right of a Decimal (Honors Only) RULE 4. Trailing zeros at the end of a number and to the right of a decimal numbers ARE significant. # # of Significant Figures 43.00 m. 4 43.00 m. 4 200.00 yr5 200.00 yr5 1.10 gal____ 1.10 gal____ 0.04500 g ____

Counting Significant Figures: Trailing Zeros (Honors Only) RULE 5. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. # of Significant Figures 25,000 in. 2 25,000 in. 2 200. yr3 200. yr3 48,600 gal____ 48,600 gal____ 25,005,000 g ____

Counting Significant Figures: Unlimited Sig Figs (Honors Only) RULE 6. 2 instances in which there are an unlimited # of sig figs. a) Counting. Ex: 23 people in our classroom. b) Exactly defined quantities. Ex: 1hr = 60 min.  Both are exact values. There is no uncertainty.  Neither of these types of values affect the process of rounding an answer.

Shortcuts to Sig Figs The Atlantic-Pacific Rule says: "If a decimal point is Present, ignore zeros on the Pacific (left) side. If the decimal point is Absent, ignore zeros on the Atlantic (right) side. Everything else is significant."

Learning Check (Honors Only) A. Which answers contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 10 5 1) 535 2) 535,000 3) 5.35 x 10 5

Learning Check (Honors Only) In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 and 22.00 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000

Significant Numbers in Calculations (Honors Only) A calculated answer cannot be more precise than the measuring tool. A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from Significant figures are needed for final answers from 1) adding or subtracting 1) adding or subtracting 2) multiplying or dividing  If you must round to obtain the right # of sig figs, do so after all calcs are complete

Adding and Subtracting (Honors Only) The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 26.54 answer 26.5 one decimal place

Learning Check (Honors Only) In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.83) 257 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7

(Honors Only) Multiplying and Dividing (Honors Only) Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Learning Check (Honors Only) A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 hr. = 60 min Factors: 1 hr. and 60 min 60 min 1 hr.

How many minutes are in 2.5 hours ? Conversion factor 2.5 hr x 60 min = 150 min 1 hr 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x _60min x 60 s = 1 day 1 hr 1 min ANSWER: 120,960 s. FINAL ANSWER (in sig figs) = 120,000 s

Scientific Notation & Your Calculator  Video Instructions- Using Calculator Video Instructions- Using Calculator

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