1. Metric Systems and Significant Figures
Mrs. Charniauskaya

3. Metric System
Scientists all over the world use the same system of units so they can communicate information clearly
This system is called Système Internationale d’Unités (SI)
Metric measurement is based on the number of 10 and makes calculations easier.

4. Base Metric Units Measurement Unit of Measurement Length Meter (m)
Mass
Gram (g)
Time
Second (s)
Volume
Liter (L or l)

5.   What unit (millimeter, centimeter, meter, or kilometer) would be most appropriate for describing the following:
      a.  The thickness of a piece of paper   ________________
      b.  The length of your pencil     _______________________
      c.  The distance from Chicago to L.A.   ________________
      d.  The height of the classroom door  ___________________
      e.  The width of a textbook   ___________________
      f.  The height of the flagpole    ____________________
      g.  The thickness of a penny   ____________________
     

6. Units
According to Système Internationale d’Unités (SI) there are base and derived units.
Base unit is based on a object or event in a physical world and is independent of other units.
Examples: meter (length of an object); kilogram (mass of an object); second (time and event takes).
Derived unit is developed from base units (made of two or more base units).
Examples:
𝒎 𝒔 , 𝒎𝒆𝒕𝒆𝒓 𝒔𝒆𝒄𝒐𝒏𝒅 (speed); 𝒈 𝒄𝒎 𝟑 , 𝒈𝒓𝒂𝒎 𝒄𝒖𝒃𝒊𝒄 𝒄𝒆𝒏𝒕𝒊𝒎𝒆𝒕𝒆𝒓 (density); 𝒄𝒎 𝟑 (volume)

7. Units SI Base Units Quantity Base Unit Time Second (s) Length
Meter (m)
Mass
Kilogram (kg)
Temperature
Kelvin (K)
Amount of substance
Mole (mol)
Electric Current
Ampere (A)
Luminous Intensity
Candela (cd)

8. Units
Derived Units
A unit that is defined by a combination of base unit is called derived unit,
Volume is the space occupied by an object.
Cubic centimeter (cm3)
Milliliter (mL or ml)
Liter (L or l)
1 cm3 = 1 ml
Si Unit
Other Unit Used
Volume m3
cm3, mL, L

9. Units of density are derived from base units of mass and length.
Units: Derived Units
Density is how much mass an object has per unit of volume, the degree of compactness of a substance.
Density of an object is equal to its mass divided by its volume.
𝑫= 𝒎 𝑽
𝑫= 𝒈 𝒎𝒍 = 𝒈 𝒄𝒎 𝟑
Units of density are derived from base units of mass and length.

10. Metric Prefix Metric Prefixes make base unit smaller or larger. Kilo
Hecto
Deka
Base Unit
Deci
Centi
Milli k H Da d c m
1000
100 10 1
0.1
0.01
0.001
103
102
101
10-1
10-2
10-3
𝟏𝟎𝟎𝟎 𝟏
𝟏𝟎𝟎 𝟏
𝟏 𝟏
𝟏 𝟏𝟎
𝟏 𝟏𝟎𝟎
𝟏 𝟏𝟎𝟎𝟎

11. Metric Prefixes Prefix Symbol Numerical Value Power of 10 equivalent
To explain the range of a measurement, scientists add prefixes to the base units.
Prefix
Symbol
Numerical Value
Power of 10 equivalent
Kilo k
1000
103 1
100
Deci d
0.1
10-1
Centi c
0.01
10-2
Milli m
0.001
10-3
Micro μ
10-6
Nano n
10-9

12. Metric Prefixes Kilo- Hecto- Deka- Base Deci- Centi- Milli-
1 cm = 10 mm
1 mm = 0.1 cm
Each unit is 10 times larger than the previous one.
Each unit is 10 times smaller than the previous one.

13. Relationship between metric units
1 kg = 1000 g
1g = 10 dg
1g = 100 cg
1 g = 1000 mg
1 km = 1000 m
1 m = 10 dm
1 m = 100 cm
1 m = 1000 mm
1 kL = 1000 L
1 L = 10 dL
1 L = 100 cL
1 L = 1000 mL

15. Uncertainty in measurements
What is the length of the blue object?
1.24 cm?
1.245 cm?
1.25 cm?
Which digits are we certain about?
Which digit we are uncertain about?
A digit that must be estimated is called uncertain.
A measurement always has some degree of uncertainty.
Uncertainty in measurements

16. Uncertainty in measurements
Measurements are performed with instruments.
No instrument can read to an infinite number of decimal places.

17. Significant figures
Scientists use significant figures to take into account uncertainty of measurement.
In measurements, the significant figures are all the digits that are known, plus a digit that is estimated.
2 sig fig.
3 sig fig.

20. Rules for Counting Significant Figures
Nonzero integers always count as significant figures.
3456 has 4 sig figs.

21. significant figures. 0.0486 has 3 sig figs.
Zeros
Leading zeros do not count as
significant figures.
has 3 sig figs.
Leading zeros

22. 16.07 has 4 sig figs. significant figures. Zeros Captive zero
Captive zeros always count as
significant figures.
16.07 has 4 sig figs.
Captive zero

23. Zeros
Trailing zeros are significant only if the number contains a decimal point.
9.300 has 4 sig figs.
Trailing zeros

24. Zeros
Trailing zeros are not significant if the number does not contain a decimal point.
9300 has 2 sig figs.
Trailing zeros

25. There are two situations in which a number has a unlimited number of significant figures:
Counted numbers are exact.
27 people in your classroom.
people in a city (all figures are significant)
Exactly defined quantities.
1 inch = 2.54 cm
1 h = 60 min

26. When scientist report measurements values they must report correct number significant figures.
The correct volume is ml, or 55.9 ml, or 56.1 ml
The values of 56 ml or ml are incorrect, because of incorrect number of sig. figs.

27. Honors Chemistry, September 9, 2016
Bell Work:
Present as a scientific notation
Present as a standard (expanded) notation
7.59 × 𝟏𝟎 −𝟑
58674 mL into L
How many sig. figs.:
689000
Learning Objective;
Be able to perform calculations with the sig. figs.
Agenda:
Bell Work
HW check and review
Quiz
Calculations with sig. figs.
Practice

28. When scientists do the calculations with the measured values they are coming up with the unreasonable number of significant figures.
Mass of an object 6.52 g
Object’s volume is 1.3 cm3
𝑫= 𝒎 𝑽 = 6.52 g 1.3 cm3 =𝟓.𝟎𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓 𝒈 𝒄𝒎 𝟑
Does the value for density look reasonable?
What do we need to do?

29. Rounding
To round a number, decide how many significant figures the answer should have.
It depends
On given measurement
On type of calculation

30. Multiplication and Division: # sig figs in the result equals the lowest number of sig figs in the calculation.
Mass of an object 6.52 g (3 sig. fig.)
Object’s volume is 1.3 cm3 (2 sig. fig.)
The answer should have 2 sig. figs.
𝑫= 𝒎 𝑽 = 6.52 g 1.3 cm3 =𝟓.𝟎𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓𝟑𝟖𝟒𝟔𝟏𝟓 𝒈 𝒄𝒎 𝟑 = 𝒈 𝒄𝒎 𝟑

31. Lowest number of decimal places
Rounding
Addition and Subtraction: The number of decimal places in the result equals the lowest number of decimal places in the calculation.
= = 18.7
Lowest number of decimal places
One decimal place
One decimal place

32. Accuracy and Precision

33. Accuracy and Precision
Accuracy refers to how close a measured value is to an accepted value.
Precision refers to how close a series of measurements are to one another.

34. Percent Error
Percent error is calculated to know how measured or calculated value is close to accepted (true) value.
%𝒆𝒓𝒓𝒐𝒓= 𝒆𝒓𝒓𝒐𝒓 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆 ×𝟏𝟎𝟎%
%𝒆𝒓𝒓𝒐𝒓= |𝒆𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 − 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆| 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆 ×𝟏𝟎𝟎%

35. Percent Composition
You have a 100 g mixture of sugar and water. What is percent composition of sugar if there are 20 g of sugar in the mixture?
Percent composition
% 𝒔𝒖𝒃𝒔𝒕𝒂𝒏𝒄𝒆 = 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒂 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒕𝒐𝒕𝒂𝒍 𝒎𝒂𝒔𝒔 ×𝟏𝟎𝟎%

36. Measurement is a quantitative observation
Measurement always has a number and a unit of measurement
2 dollars
2 cents
2 g
2 kg