Measurement and Scientific Notation

Measurement and Scientific Notation

1  Review of Scientific Method


Repeat as needed.


Additional information is available.

2  Observation

Qualitative
- No measurements performed.

    Ex.         ¯ It is hot today.
 The powder was red.
 He was heavy.

Quantitative
- Requires measurements.

    Ex.         ¯ It is 43°F today.
 The powder absorbed 475 nm light.
 He weighed 276 pounds.

3  Systems of Measurement


Which is better:
   English or metric system?



Neither.
Both are systems based on arbitrary standards.

4  Units of Convenients

Units of measurement are chosen primarily for convenience of user.


For example:

5  A New Arbitrary Measure



Let's use the width of the room as our base unit for measuring length. We will refer to this unit as one "room".

6  Acceptance

The 'room' unit that we have derived is inherently no better or worse than inches, meters, cubits, ...



The primary disadvantage of this unit is that that is not a standard, well-accepted, reproducible definition of a 'room'.



We could define room in terms of feet, inches, meters, ..., but this makes room a secondary standard based on the primary standard of feet, inches, meters, ...

7  Metric System

Advantages

Almost all scientific work is reported in metric units because these are so well accepted worldwide. This makes experiments much easier.

8  Metric Problems

Disadvantages

(The problem of converting between two different sets of units is not limited to the metric system.)

9  Metric Prefixes

Prefix Abbrev. Size Sci. Notation
mega M 1,000,000 106
kilo k 1000 103
- 1 100
deci d [ 1/10] 10-1
centi c [ 1/100] 10-2
milli m [ 1/1,000] 10-3
micro m [ 1/1,000,000] 10-6

10  Orders of Magnitude

Metric system based on powers of 10.


(Classroom display of orders of magnitude).


Conversion between units simply means moving decimal point.



Ex.

1,560,000 mm = 156 cm = 1.56 m = 0.00156 km


Note: It takes fewer big units than small units.

11  Metric Conversions

To convert between metric units:


  1. Find order-of-magnitude difference between prefixes.

  2. This difference indicates how much to shift decimal point.

  3. When going from smaller to larger units, make number smaller.

  4. When going from larger to smaller units, make number larger.

12  Metric Examples

Perform each of the following conversions:


156 cm =    ? m1.56 m
156 m = *2   ? cm15,600 cm
0.68 cm = *3   ? mm6.8 mm
63.7 mm = *4   ? mm0.0637 mm

13  Metric Units

The following base units are defined in the metric system.

Physical Quantity Unit Abbrev.
Mass kilogram kg
Length meter m
Time second s
Temperature Kelvin K
Electric current ampere A
Amount of substance mole mol
Luninous Intensity candela cd

14  Metric Equivalents

The following table lists some very approximate conversions between metric and English units.

English unit Similar Metric value
yard meter
inch 2.5 cm
mile 1.6 kilomter
quart liter
pound [ 1/2] kilogram
ounce 30 grams

15  Scientific Notation

See also textbook page 11

Convenient for very large or very small numbers.

Ex. 1 gram of water contains


33,400,000,000,000,000,000,000 molecules


or


3.34 x 1022 molecules

16  Sci. Notation Explained

In scientific notation,

number x 10exponent

number
- must be \geqslant 1 and < 10
exponent
- indicates position of decimal point

Positive (+) exponents indicate large numbers (>1)
Negative (-) exponents indicate small numbers (<1)

17  Sci. Notation Conversions

For each of the following, convert between scientific and decimal notations.


2.54 x 103 = 2,540
2.54 x 10-3 = 0.002 54
15,280 = 1.528 x 104
0.0000638 = 6.38 x 10-5

18  English/Metric Equivalences

Often we need to convert between English and metric units.

This requires conversion factors.

1 inch  = 2.54 cm
1 quart  = 0.946 L
1 gram  = 0.0353 oz
1 kilogram  = 2.20 lbs


There is no reason to memorize these factors. See also textbook Appendix 1 (p. 493).

19  Conversion Factors

This method relies on two basic ideas.

  1. Multiplication by 1 doesn't change a number.

  2. Any non-zero value divided by itself is one.

Given:

2.54 cm = 1 in


then

[ 2.54 cm/1 in] = 1 = [ 1 in/2.54 cm]

20  Factor-Label Method

Problem: How many cm in 15.7 inches?


Solution:

1 inch = 2.54 cm

15.7 inches x [ 2.54 cm/1 inch] = 39.9 cm

21  Conversion Rules

Use the following guidelines to perform exact conversions between units.


  1. Use common sense to guess the answer (Really).

  2. Look up the appropriate equivalence (conversion) values.

  3. Write down the known quantity with units shown

  4. Setup conversion factor as: [ unit you want/unit to get rid of]

  5. Multiply known quantity by conversion factor.

  6. Verify that answer agrees with common sense.

22  Another Example

Problem: How many inches in 15.7 cm?


Solution:

1 inch = 2.54 cm

15.7 cm x [ 1 inch/2.54 cm] = 6.18 inches



File translated from TEX by TTH, version 3.02.
On 16 Jan 2002, 16:50.