1. UNDERSTANDING AND USING THE METRIC SYSTEM

2. INTERNATIONAL STANDARDS EASE OF RECORDING C. EASE OF CALCULATIONS
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE
INTERNATIONAL STANDARDS
EASE OF RECORDING
C. EASE OF CALCULATIONS
II. THE IMPORTANCE OF PREFIXES
A. MILLI - TO KILO - THE COMMONLY USED PREFIXES
B. CONVERTING UNITS BY MOVING THE DECIMAL

3. I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

4. I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
A. INTERNATIONAL STANDARDS… *
* All metric system units are based on specific definitions which are internationally known standards and are reproducible
Volume =1.0 liter
*THAT IS, MEASUREMENTS ARE THE SAME ALL OVER THE WORLD… REGARDLESS OF COUNTRY OR LANGUAGE
Length =1.0 meter
Mass = 1.0 kilogram

5. I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
B. EASE OF RECORDING MEASUREMENTS… *
All metric system units are based on TENS, that is subdivisions of the main units are based on ‘tenths’, ‘hundreths’, thousandths’, etc.
.1 unit
One whole unit

6. Subdivisions can be divided again and again for more precision…
.1 unit
.01 unit
.001 unit
(Again by tenths)

7. This means that very precise measurements can be recorded as “DECIMAL VALUES” !!
.1 unit
.01 unit
.001 unit
EXAMPLES:
2.351 liters
.802 meters
5.45 centimeters
9.023 meters
5.613 grams

8. This is a huge advantage over the older “fraction” based systems…
Recording measurements is too complex, prone to errors…
1/12 unit
1/16 unit
1/2 unit
Examples:
2 miles, 235 yards, 2 feet, 7 inches
2 pounds, 8 9/32 ounce
4 gallons, 1 quart, 5 ¾ ounces
5 yards, 2 feet, 7 1/16 inch

9. I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
C. EASE OF PERFORMING MATH FUNCTIONS…
Examples:
1.62 kg
(5.4 cm) (8.65 cm) (362 cm)
Is far easier to do than…
(1 lb., 9 ½ oz.)
(11 ¾ in)(1 ft.4 11/16 in)(1 yd.1ft 1½ in)

10. II.UNITS OF MEASUREMENT

11. II.UNITS OF MEASUREMENT
THE “BASE” UNITS:
SOME QUANTITIES HAVE TO BE THE STARTING POINTS…
THAT IS, SOME BASIC UNITS HAVE TO BE DEFINED…
#1:
The unit of LENGTH: the METER– originally defined as ONE TEN-MILLIONTH the distance from NORTH POLE TO EQUATOR

12. II.UNITS OF MEASUREMENT
THE “BASE” UNITS: #2
1 DECIMETER
The unit of VOLUME: the LITER… defined as the space occupied by a cube measuring .1m x .1m x .1m (1 cubic decimeter—1.0 dm3)
1 DECIMETER
1 liter = 1dm3
1 DECIMETER

13. II.UNITS OF MEASUREMENT#3
THE “BASE” UNITS:
The unit of MASS: the KILOGRAM… defined as the mass of 1.0 liter of pure water at 4.0oC…
1.0 kilogram = mass of 1 liter of H2O

14. II.UNITS OF MEASUREMENT#4
THE “BASE” UNITS:
The unit of TIME: the SECOND…

15. III. THE IMPORTANCE OF PREFIXES
A. FROM MILLI TO KILO
B. MOVING THE DECIMAL

16. III. THE IMPORTANCE OF PREFIXES
A. FROM MILLI TO KILO
THE PREFIXES USED ARE COMMON TO ALL TYPES OF MEASUREMENT:
EXAMPLES:
milligram millimeter milliliter milliamp millisecond
gram meter liter volt
kilogram kilometer kiloliter kilojoule

17. III. THE IMPORTANCE OF PREFIXES
A. FROM MILLI TO KILO
This prefix changes the base into a unit 1/100 as large as the base
The base of any defined or derived unit
This prefix changes the base into a unit 1/1000 as large as the base
Important prefixes to know:
This prefix changes the base into a unit 1/10 as large as the base
A prefix that makes a unit 10x larger than the base
MILLI .001
CENTI .01
This prefix changes the base into a unit 100x larger
DECI .1
This prefix changes the base into a unit 1000x larger
BASE UNIT
DECA 10x
HECTA 100x
KILO 1000x

18. Come up with a sentence to order the prefixes!
Milk
Chocolate
Drinking
Died
Henry
King
MILLI My
Cat
Died
Drinking
Holy
Ketchup
Come up with a sentence to order the prefixes!
CENTI
How are we going to remember these?
DECI
BASE UNIT
DECA
HECTA
KILO

19. Understanding prefixes…
Let this entire box represent 1.0 liter…
1/10th (.1) of the box could be called a ‘deciliter
How many of these would be in 1 liter?
Did you do a mental short-cut and just tack on a zero? That is, just slide the decimal over and fill in with zero?
To get those values, did you just multiply by 10?
In 5 liter?
Did you answer 10?
Who thinks 50?

20. Understanding prefixes…
If the measured value gets too big (or too small), change to a more convienent unit by moving the decimal to the left or to the right, then fill in zeros… that’s really all there is to conversions!!
That is the secret of converting to more convienent units within the metric system!!

21. Understanding prefixes…
Simply move the decimal 3 places to the right and fill in with zero’s (make a number 1000x bigger…)
If this little box represents 1/1000th of the liter, what could it be called?
How many of these are in the 1.0 liter?
What did you do to get that answer?
1000?
Milliliter?? 1.
= 1000 ml

22. To change to a smaller unit move the decimal to the right and fill in the zero’s
To change to a larger unit move the decimal to the left and fill in the zero’s
MILLI
CENTI
DECI
BASE UNIT
DECA
HECTA
KILO

23. That is…
That is…
Up and to the RIGHT
Down and to the LEFT

24. That is…
That is…
Up and to the RIGHT

25. That is…
Down and to the LEFT

26. SAMPLE PROBLEM:
AN ANSWER TO A CALCULATION GAVE A VALUE OF “54,500 METERS”
ALTHOUGH ‘CORRECT’, THE VALUE IS LARGE AND CUMBERSOME; IT CAN BE SHORTENED AND REDUCED TO A SMALLER VALUE BY A SIMPLE CONVERSION…
METERS are 1000x smaller than KILOMETERS… therefore the converted value will be 1/1000th the original! That is, move the decimal 3 places to the left!!!
“54,500 METERS” can be shortened by changing the unit from ‘meters’ to ‘kilometers’

27. MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
To change to a larger unit move the decimal to the left and fill in the zero’s
REMEMBER…
MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
METER
KILOMETER

28. MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
Use the chart…
MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
54,500
5450.0
545.00
54.500

29. MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
REMEMBER…
MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
METER
KILOMETER
54,500 METERS
= 54.5 KILOMETERS

30. SAMPLE PROBLEM:
A physics student has this value for the current in a circuit:
14.3 amps
However, the formula in which she has to use the value calls for the current in MILLIAMPS…
A quick conversion by moving the decimal point is easy:

31. MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
milliamps
amps
To change to a smaller unit,
move the decimal to the right and fill in the zero’s

32. MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
Use the chart…
MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
14300
1430
143
14.3

33. SAMPLE PROBLEM:
14.3 amps
Converts to: .
14.3
= milliamps

34. SAMPLE PROBLEM:

35. SAMPLE PROBLEM:

36. Metric Activity 1. Length of your shoe in mm 2. Your height in dm
3. Width of the hallway in meters
4. Circumference of your head in cm
5. Area of your desk in cm2

37. Shoe (mm)
Height (dm)
Hallway (m)
Head (cm)
Desk (cm2)
290
180 3 55
7830
315
7.5
2.7 51
8056
320
17.2
58.5 17
2.99 57
330
18.4
3.3 63
17,422.5
300
17.6 60
240
12.1
2.69
270
14.9
2.67
51.5
8,258.25
15.3 54
3000
1600
2.5
460
16100
220
15.7
2.31 25
1560 58
16695
248
1400
301
16.9 50
310 18
260
165
164
15812
163
3.1
54.5
210
15.5
95.6

38. Now find... 1. Class shoe length in meters 2. Average height in cm
3. Average head size in dm

39. 1. Class shoe length in meters 2. Average height in cm
Shoe (mm)
Height (dm)
Hallway (m)
Head (cm)
Desk (cm2)
225
14.85
3.055 54
16,192
325
17.4
3.01
56.3
250
15.8
3.06 55
14,352
320
18.8
3.08
57.5
8082.5
15.5
3.02 48
300
17.8 56
1620
16.2
3.5 57
7750
240
15.0 17
3.1
58.5
7,705
1. Class shoe length in meters
2. Average height in cm
3. Average head size in dm

40. SAMPLE PROBLEM:

41. 65,000,000,000,000 km
Sometimes numbers can still be quite large or quite small
For this scientists use scientific notation mm

42. 65,000 = 6.5 x10 4 Scientific Notation
The number must be expressed so only a single digit remains to either the right or left of the decimal point
65,000 = 6.5 x10 4

43. 65,000 = 6.5 x10 4 Scientific Notation
The power of 10 is the number of places the decimal place must be shifted
65,000 = 6.5 x10 4

44. 65,000 = 6.5 x10 4 Scientific Notation
If the decimal point is shifted left the exponent is positive
65,000 = 6.5 x10 4

45. 0.0001 = 1.0 x10 -4 Scientific Notation
If the decimal point is shifted right the exponent is negative
= 1.0 x10 -4

46. Scientific Notation -3 ?
0.007 = 7.0 x 10
4,500,000 = 4.5 x 10 6 ?
167,000 = =
1.67 x 105
4.6 x 10-5