1. 5. The metric system (SI system) is based on powers of 10.
UNITS OF MEASUREMENTS
1. A quantity is something that has magnitude, size, or amount.
2. In 1960 the General Conference on Weights and Measurements decided all countries would use the International System of Units (Metric) system as the standard units of measurements.
3. Almost every country uses the metric system for daily calculations except the United States and Great Britain.
When using the metric system commas are not used with numbers because other countries use commas to represent a decimal point.
Ex. 75, 000 is written
is written
5. The metric system (SI system) is based on powers of 10.

2. 5. There are seven fundamental units in the metric system
5. There are seven fundamental units in the metric system. All other units are derived from these units.

4. 6. A derived unit is a combination of fundamental units.
Example: The unit for force is the Newton = N= kg x m / s2
Example: The unit for energy is the Joule = force x length = Nm
= kg x m2 / s2
Example: Area is calculated L x W = m x m = m2
7. If a unit is not a fundamental unit, it is a derived unit.

5. What about volume?
Notice that liter ( the unit for volume) is not a fundamental unit.
To determine the volume of an object a length must be measured. So,
volume is derived from length.
Volume = l x w x h
= m x m x m
= m3

6. ml = 1 cm3
A 1 cm x 1 cm x 1cm cube will hold 1 ml of liquid.
1 ml = 1cm3 = 1 cc (cubic centimeter)
ml = 1 Liter cm3 = 1 L

7. cm3 = 1000 ml ml = 1 Liter cm3 = 1 L

8. Why Metric?

10. 1.3 Scientists Measure
Physical Quantities

11. A physical quantity must include:
A NUMBER + A UNIT

12. 13. The metric system provides a standard unit of measurements used by all countries. Is the man 92.5 m, 92.5 cm, 92.5 in, or 92.5 ft?

13. How many centimeters are in an inch?

16. UNCERNTAINTY IN MEASUREMENTS AND
SIGNIFICANT FIGURES
1. Whenever a measurement is taken, the last digit is uncertain and estimated.

18. Which clock would be the most accurate?

19. RULES FOR COUNTING SIGNIFICANT FIGURES
All nonzero digits are significant.
Ex g significant figures.
25 g significant figures
26.42 g 4 significant figures
All zeros between non zero digits are significant.
Ex L significant figures
L 5 significant figures
Decimal numbers that begin with zero.
The zeros to the left of the first nonzero number are not significant.
Ex L 3 significant figures
L 2 significant figures

20. Decimal numbers that end in zero.
The last zero is significant Ex g significant figures
g significant figures
8.0 g significant figures
Non decimal numbers that end in zero The zero is significant only when a written decimal is shown Ex g significant figures
900 g significant figure
90. g significant figure

21. Determine the number of significant figures.
PRACTICE
Determine the number of significant figures.
65.42 g _____
385 L _____
0.14 ml _____
709.2 m _____
kg _____
400 dm _____
260. mm _____
0.47 cg _____
km _____
7.0 cm _____
36.00 g _____
kg _____
L _____
cm _____ 4 3 2 6 1 7 5

22. Rounding Significant Figures
Sample: round to 3 significant figures (sf) _______
round to 1 sf ______
round to 3 sf ______
round to 4 sf ______
round to 2 sf ______
Practice
Round to the indicated number of significant figures.
24 km to 2 sf _____
L to 2 sf _____
2.68 g to 2 sf _____
4.165 L to 3 sf _____
2.68 g to 2 sf _____
8.35 ml to ml 2 sf _____
12 ml to 1 sf _____
to 2 sf _____

23. MULTIPLYING AND DIVIDING SIGNIFICANT FIGURES
The arithmetic product or quotient should be rounded off to the same number of
significant figures as in the measurement with the fewest significant figures.
???????????????????????
Keep the smallest number of significant figures.
Examples:
2.86 g x 2.0 g = g the answer is 5.7 g
38 ml / 1.25 ml = 30.4 ml the answer is 30. ml
0.596 g x g = g the answer is g

24. Adding and Subtracting Significant Figures
1. The arithmetic result should be rounded off so that the final digit is in the same place as the leftmost uncertain digit.
Ex g g = g the answer is 116 g
g – g = g the answer is g

25. 21.50 g / 4.06 cm x 1.8 cm x 0.905 cm = ____________
PRACTICE
9.40 cm x 2.6 cm = ____________
8.08 dm x dm = ____________
4.07 g g = ____________
m m m ____________
1.50 g / 2 cm3 = ____________
g / ml = ____________
21.50 g / 4.06 cm x 1.8 cm x cm = ____________
24 cm dm g m g/ml
g/ml g/cm3

26. Convert 21300000 to scientific notation
2.13 x 10 7
2. Convert to scientific notation
2.0 x 10-9
Practice: Convert to scientific notation
900
750000
250000
9 x x x x 104
x x x 105

27. CALCULATOR PRACTICE 1. 3 x 1055 x 7.56 x 1015 = 2 x 10 71
Practice: Don’t forget to keep the correct number of significant figures.
2.6 x x =
8.3 x x =
7.43 x x 104 =
(3 x 10 5 )( 2 x 107 ) =
(7.5 x 106 )/(4 x 10-2) =
x 102
x 10-5
x 105
4. 6 x 107
5. 2 x 108

28. BACK TO ROUNDING SIGNIFICANT FIGURES INVOLVING
SCIENTIFIC NOTATION
1. Round 400 g to 3 significant figures.
4.00 x 102
2. Round to 2 significant figures
3.0 x 10-6
Simply change the number to scientific notation when going from a smaller number of significant figures to a larger.

29. IMPORTANT REMINDER:
Your calculator does not know how to do significant
figures. YOU must report numbers using the correct
number of significant figures.
If you trust the number your calculator gives you, you
might get the answer wrong!!!! TI or Casio don’t care
what grade you get on the test.
Figure: 02-03UN13
Title:
Rounding off numbers
Caption:
Calculators often display more digits than are justified by the precision of the data.
Notes:
Only use the meaningful digits in a measured or calculated quantity.
Keywords:
rounding numbers, precision

30. ACCURACY AND PRECISION
Accuracy is the closeness of the measurements to the true or accepted
value.
The accuracy of an instrument can only be determined if the true or
or accepted value for the measured item is known.
3. Precision refers to the agreement among the numerical values of a set of numbers.

31. Picture 1 is accurate and precise
Picture 2 is precise but not accurate.
Picture 3 is neither accurate or precise.

32. 4. Scientific instruments should be accurate
4. Scientific instruments should be accurate. If instruments are accurate,
they are also precise.
5. If an instrument is precise, it may not be accurate.

33. Dimensional Analysis
(Factor Label)
1. Dimensional Analysis (factor label) is a problem solving technique.
2. This method of problem solving uses conversion factors.
3. A conversion factor is a ratio that is equal to one.
Example:
4 quarters = $1
24 hours = 1 day
185 days = 1 student school year

34. Calculation Corner: Unit Conversion
1 foot
12 inches
12 inches
1 foot
“Conversion factors”

35. Calculation Corner: Unit Conversion
1 foot
12 inches
12 inches
1 foot
“Conversion factors”
12 inches ( ) ( )
3 feet
= 36 inches
1 foot

36. Calculation Corner: Unit Conversion
1 foot = 12 inches
1 foot
= 1
12 inches
12 inches
= 1
1 foot

37. Calculation Corner: Unit Conversion
1 foot = 12 inches
1 foot
= 1
12 inches

38. Calculation Corner: Unit Conversion
1 foot = 12 inches

39. Fahrenheit
Celsius
32°F
0°C

40. Fahrenheit
Celsius
Kelvin
32°F
0°C
273K
-459 °F
-273 °C
0 K

41. Fahrenheit
Celsius
Kelvin
212 °F
100 °C
373K
32°F
0°C
273K
0 K