1. Ch 3 Scientific Measurement

2. Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured.
Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

3. Percent Error tells you how far away you are from the accepted value
Percent error = observed – accepted x 100
accepted value
*note: observed value is also the experimental value
Example: Calculate the percent error of a measurement of .225 cm if the correct value is .229 cm.
Ans %

4. Ex #2/ A student measures three trials of density of gold: 19
Ex #2/ A student measures three trials of density of gold: g/mL, 18.9 g/mL, and g/mL. If gold’s actual density is g/mL, what is the percent error?
Ans.  -1.55%

5. Error (or uncertainty) exists in any measurement
Error (or uncertainty) exists in any measurement. The amount of uncertainty is determined by finding half of the smallest increment in the measure.
Ex/ for the 10 mL graduated cylinder the uncertainty of each measurement is + or mL since the smallest increment is .1 mL
Significant Figures in a measurement consists of all the digits known with certainty plus one final digit which is uncertain or estimated.

6. Rules of Significant Numbers and Zeros
1. All non-zero numbers in a measured quantity are significant. Ex: 2.34 m= 3 significant figures 2. Zeros appearing between non-zero digits are significant. Ex: 2.04 km = 3 SFs m= 5 SFs

7. 3. Zeros appearing in front of non-zero digits are not significant
3. Zeros appearing in front of non-zero digits are not significant. Ex: m= 4 SFs 4. Zeros at the end of a number and to the right of the decimal are significant. Ex: kg = 5 SFs kg = 5 SFs

8. 5. Zeros at the end of a number and to the left of the decimal may or may not be significant. It depends on whether it was measured or if it is a placeholder. NOTE: If there is a decimal after the zeros, then they are significant Ex: m = 4 SFs NOTE: If there is no decimal after the zeros, then they are not significant. Ex: 1000 m = 1 SF

9. How many significant figures are in each of the following measurements?
1) g Ans. 4 SF’s 2) 6,330. m 3) 6330 m Ans. 3 SF’s 4) mg 5) mg Ans 5 SF’s

10. Rules for Rounding SFs 1. Greater than 5 : increase by 1
If the digit following the last digit to be retained is: *examples rounded to 3 SF’s
Greater than 5 : increase by 1
EX/ g = g
2. Less than 5 : Stay the same
EX/ g = g
3. 5, followed by a nonzero digit: increase by 1
EX/ g = 12.3 g

11. Rules rounding continued
If the digit following the last digit to be retained is:
4.) 5, not followed by nonzero digit, and preceded by an odd digit :
increase by 1 “round up”
Ex/ g = 4.64 g ( 3 sig figs)
5.) 5, not followed by nonzero digit, preceded by an EVEN digit:
stays the same
Ex/ mL = mL

12. Rules for Calculations with SF’s
Adding or Subtracting Significant Figures
When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right.
Ex: m  2 decimal places
m  4 decimal places m
final answer is 2.83 m

13. Multiplying or Dividing Significant Figures
 When multiplying or dividing with SFs, the answer can have no more SFs than are in the measurement with the fewest number of SFs.
Ex: m = DV
2.4 g/mL x mL = g
Final answer is 38 g with 2 SFs

14. Scientific Notation are the writing of very large or small numbers in the form M x 10n, where M is a number greater than or equal to one, but less than 10, and n is a whole number.
Ex: g = 5.2 x 109 g
Ex: g = 2.3 x 10-5 g

15. Practice: copy the question & answer
4.52 x 104g (4.5 x 104cm)(2.7 x 103cm) +2.7 x 103g 4.52 x 104g / 2.7 x 103mL

16. Check your answers
4.52 x 104g (4.5 x 104cm)(2.7 x 103cm) = +2.7 x 103g 1.2 x 108 cm2 4.8 x 104 g 4.52 x 104g / 2.7 x 103mL = 1.7 x 101 g/mL

17. Units of Measurement

18. International System of Units
Called the SI system (or Metric System)
established in France (Systeme Internationale d’Unites)
1960 revised for International scientific agreement.
SI system is simple because it is based on factors of 10 

19. 7 Base Units Quantity Measured Unit abbreviation length meter m
mass gram g
time second s
electric current ampere A
temperature Kelvin K
amount of substance mole mol
luminous intensity (light) candela cd

20. SI Prefixes
k kilo 1000x’s (1 km = 1000 m) h hecto 100x’s (1 hm = 100 m) da deka 10x’s (1 dam = 10 m) Base Units (m, g, s, mol, cd, A, K) d deci 1/10 (10 dm = 1 m) c centi 1/100 (100 cm = 1 m) m milli 1/1000 (1000 mm = 1 m)

21. Converting one unit to another
Two ways:
1. Use a conversion factor that expresses the relationship between the units.
Ex/ 1 m = 100 cm
Two conversion factors: __1 m__ or cm__
100 cm m
How many meters in 550 cm?
550 cm x __1 m____ = m
100 cm

22. 2. Convert units by shifting the decimal place.
King Henry’s daughter begins dance class Monday.
550 cm = __________m
6.77 hg = __________ dg
k h da B d c m
Start with given units and jump to desired units. Move decimal same direction as number of jumps.

23. Metric Conversions practice:
Copy this practice and turn in when completed: 1) 40.0 m= _________cm 2) 40.0 m= __________km 3) m= _________dam 4) m= __________hm 5) .005 m= ___________mm 6) .005 km= ___________m 7) .005 km= __________dm 8) .005 mm= __________dam 9) 16 km=___________dam 10) 16 km ___________cm

24. Metric Conversions practice: Key
40.0 m= __4.00 x 103__cm (4000 cm)
40.0 m= ___.0400____km
32.41 m= ___3.241__dam
32.41 m= ___.3241___hm
.005 m= ______5____mm
.005 km= _____5_____m
.005 km= ___5 x 101__dm (50 dm)
.005 mm= _5 x 10-7___dam ( )
16 km=____1600___dam
16 km _ or 1.6 x 106_cm

25. Derived Units:
come from base units (multiplying or dividing base units) For example: Volume (mL) is considered a derived unit. Using water to fill a cube that is 1 cm on each side: Volume= l x w x h vol= 1 x 1 x 1= 1cm3 1 cm3= 1 mL in a graduated cylinder. 1 L = 1000 mL = 1000 cm3 *The mass of 1 cm3 of water equals 1 gram as well. 1 cm3= 1 mL= 1g