Ch. 3, Scientific Measurement

Measurement : A quantity that has a and a. Like 52 meters.

Scientific Notation Writing long numbers as smaller ones to a power of ten. = 1.4 x 10 6 = 1.4E = = 5.6E-4 15,093,000 = x 10 7 =

Accuracy vs. Precision * : How close a measurement comes to the value. * : How close a series of measurements are to.

Determining Error of a measurement = Experimental Value - Accepted Value – Can be positive or Percent Error = error / accepted value * 100% – or – Always Example, you measured 99 cm, but it is 100 cm.

: The digits in a measurement that are known plus one that is not known. – Filled 43.1 mL

Rules for Sig Figs Non-Zero Numbers are always significant – Ex).236 m has sig figs. Zeros between non-zero numbers are significant. – Ex) 7003 m and m each have sig figs. Leftmost zeros are not significant – Ex) m, 0.42 m, and.073 m each have sig figs. Rightmost zeros are significant if they come before or after a period. – Ex) m, m, and m each have sig figs.

Rules for Sig Figs Rightmost zeros with no decimal points are no significant. Ex) 300 m has sig fig. Exactly defined quantities have an number of sig figs. Seen most when converting between measurements. 60 min = 1 hour, 100 cm = 1 m each have an unlimited number of sig figs.

Is a Zero a Significant Number or Not? 504 L.06 mL 50.0 m 7,000 km

Sig Figs in Calculations: Calculations be more precise than the precise measurement. Addition or subtraction - Round the final answer to the same number of decimal places as the measurement with the number of decimal places. – the last “shared column” m m = 18.7 m

Sig Figs in Calculations: Multiplication or Division - The final answer should have the number of sig figs as the measurement that has the number of sig figs m x 8.4 m = 21 m

In this class, delay rounding until the very end. (3.449L L) * 8.779L / 5.2L = 17L

How much of something you have is given by Units. Like centimeters, kilometers, etc. is the standard measurement system for science. International System of Units

* The five SI units used most by chemists are: Distance = (m) Mass = kilogram (kg) Temperature = (K) Time = second (s) Volume = liter (L) Amount = (mol).

Prefixes can be used in front of units for powers of 10.

= how much “stuff” is in something. How much matter is in something. = the pull on something by gravity. If I go to the moon, which changes and which stays constant? - changes, stays the same.

Temperature: Celsius and Kelvin are units of temperature that are the, just shifted. K = C Water freezes at 0 C and at K. Absolute Zero = 0 K; a K value will never be negative.

*Energy * - The ability to do work or produce heat. (J) is the SI unit of energy. (cal) is another unit of energy. 1 J =.239 cal

Conversions Convert 7 mm to m. Convert 12.4 Mm to cm.

Convert 7 km/ms to m/s An experiment asks students to measure 1.50 g of Cu wire. All we have is a 40.0 g spool of Cu. How many students can do the experiment?

*Density * = mass / volume What is the density of 2 g of salt in a volume of 4 L? What is the density in g/L of 5 kg of salt in a volume of 6 mL?

If silver has a density of 10.5 g/L, what is the volume of a silver coin that has a mass of 14 g?

Density as temperature increases. D=m/v As T increases, V. Therefore, density decreases.

Example Problems!!!

1. How many sig figs in: 1.480* E3 2. Perform these calculations and come up with answers that have the correct number of sig figs: E3 / E3 * 3 3. Convert 3.4 ng into kg. 4. Convert 7E3 cm into Mm. 5. What is the mass if a substance with a density of 4.5 g/L has a volume of 3 L?

6. How many sig figs in: Convert 3 kg into g. Convert 34 cm into m. Convert 4 m into cm. 8. You have a 4 kg box. You measure it to be 5.8 kg. What is the error? The % error? 9. What is the difference between mass and weight? Accuracy and precision?

11. Put 5,009,000,000 into Scientific Notation 12. Put into Scientific Notation. 13. Put 8.7 * into a regular number.

14. Which is the largest amount? A. 2*10 2 g B. 30 kg C. 45 mg D. 190 g 15. Convert 40 Kelvin into Celsius 16. Convert 99 Celsius into Kelvin.

More from Chp 3 I. Using Measurements

A. Accuracy vs. Precision - how close a measurement is to the accepted value - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

C. Significant Figures Indicate precision of a measurement. Recording Sig Figs –Sig figs in a measurement include the _ digits plus a final digit –(See page 24) 2.32 cm

1) How many sig figs after we estimate? 2) Now how many?

C. Significant Figures Counting Sig Figs –Count all numbers EXCEPT: _______________zeros Trailing zeros _________________ a decimal point -- 2,500

, C. Significant Figures Counting Sig Fig Examples , sig figs

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

C. Significant Figures Calculating with Sig Figs (con’t) –Add/Subtract - The # with the decimal value determines the place of the last sig fig in the answer mL mL 7.85 mL  3.75 mL mL 7.85 mL

C. Significant Figures Calculating with Sig Figs (con’t) –Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

C. Significant Figures 5. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL g g g 

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

D. Scientific Notation 7. 2,400,000  g kg 9. 7  km  10 4 mm Practice Problems

D. Scientific Notation Calculating with Sci. Notation (5.44 x 10 7 g) / (8.1 x 10 4 mol) = Type of your calculator: 5.44 EE 7 / 8.1 EE 4 =

E. SI Units QuantityBase UnitAbbrev. Length Mass Time Temp meter kilogram second kelvin s K Amountmole Symbol l m t n

E. SI Units mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 BASE UNIT

F. Derived Units Combination of base units. (m 3 or cm 3 ) –length  length  length D = MVMV 1 cm 3 = 1 mL 1 dm 3 = 1 L  (kg/m 3 or g/cm 3 )  mass per volume

Problem-Solving Steps 1. _ 2. Plan 3. Compute 4. _

Density An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = D = M = ? WORK :M = M =

Density A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = V = ? M = WORK : V = V =

SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 move left move right BASE UNIT

SI Unit Conversions King __doofus can milk many newts. k__ d c m m n kilo, deci,, milli,, What’s yours?

= SI Prefix Conversions NUMBER UNIT NUMBER UNIT 532 m = _______ km

SI Prefix Conversions 1) 20 cm = ______________ m 2) L = ______________ mL 3) 45 m = ____ mm 4) 805 dm = ______________ km

Dimensional Analysis Steps: 1. Identify starting & units. 2. Line up conversion factors so units. 3. Multiply all numbers & divide by each bottom number. 4. Check units & answer.

Dimensional Analysis Lining up conversion factors: 1 in = 2.54 cm 2.54 cm 1 in = 2.54 cm 1 in 1 in = 1 1 =

Dimensional Analysis How many milliliters are in 1.00 quart of milk? (1L = qt) 1.00 qt qtmL 

Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3. (1 kg = 2.2 lbs) lbcm lb

Dimensional Analysis 5)Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm) 8.0 cm cmin