Chapter One Measurement and the Metric System

The Importance of Measurement and Mathematics in the Physical Sciences Also since numbers are much less ambiguous than words, our hypotheses can be stated in a way so that they may be tested by many persons which increases our confidence in the results. Measurement allows us to express our observations in numerical form. This allows others to make the same observation and compare the results. This leads to increased confidence that the observation is valid. Well-confirmed observations are called facts. The importance of observation in science would be difficult to exaggerate. Every statement or idea in science must be checked and rechecked by observations of nature, and if the idea conflicts with the observation, the idea must yield and be modified or cast aside. No appeal to "common sense", authority, or anything else can save an idea that conflicts with observation.

Having our observations, hypotheses, and conclusions expressed numerically allows them to be manipulated using the rules of mathematics. 1. We can replace long verbal statements with more concise mathematical expressions. For example: Newton’s Second Law of Motion can be expressed in words as follows: The magnitude of the acceleration of an object is directly proportional to the net force applied to the object, and inversely proportional to the object's mass. The direction of the acceleration is the same as the direction of the net force. The statement above can be expressed mathematically as:

2. Once an idea is expressed in mathematical form, we can use the rules (axioms, theorems, etc.) of mathematics to change it into other statements. If the original statement is correct, and you follow the rules faithfully, your final statement will also be correct. For example: the acceleration of an object can be expressed mathematically as: We can multiply both sides of the equation by “t” to get:

What does it mean to measure something? Suppose you wanted to measure the length of a table. What would be your first step? Choose a standard unit of length that is appropriate for the measurement. Meter stick Yard stick Ruler, etc. What would be your next step? Compare the meter stick with the table, i.e. place one end of the meter stick at one of the table, mark the location of the other end, move the meter stick to begin at the mark, continue to the other end of the table, counting as you go? Let’s choose the meter stick. Let’s say that we placed the meter stick 5 times. The final step is to record the measurement. The length of the table is:5 meters or 5m

All measurements have two parts: A numerical part that gives the result of the comparison between the chosen unit and the thing being measured. A unit part which tells what standard unit was used to make the measurement. Both parts must be recorded if the measurement is to be useful. In this chapter we will concentrate on the unit part of measurements. We will begin with the fundamental units from which all other units are derived.

Five Properties of Nature Five Fundamental Properties of Nature *Pound is actually a unit of weight, the unit of mass in the FPS system is the slug, but it is rarely used. We will see later that mass and weight are related. *System used universally by scientist.

Derived Properties ( Units depend on operational definition) Area Volume Density Speed Acceleration

Force Work

Metric Prefixes Used to adjust the size of a unit to best fit the quantity being measured. PrefixSymbolMultiplies byPower of 10 notation MegaM1,000,000 kilok1,000 centi c0.01 millim0.001 micro Prefixes that enlarge a unit Prefixes that reduce a unit

Scientific Notation Method of writing numbers using powers of ten rather than zeros to place the decimal. ^ 8 decimal places to the right Distance from the earth to the sun Mass of an electron ^ 22 decimal places to the left

Using Scientific Notation on a Calculator or

Expressing Measurements in Different Forms Numerical Part: Standard Decimal, Scientific Notation Unit Part: With/Without Metric Prefix standard decimal, w/o metric prefix convert numerical part to scientific notation replace X 10 3 with corresponding metric prefix, kilo…k

standard decimal, w/o metric prefix convert numerical part to scientific notation replace X with corresponding metric prefix, micro… 

standard decimal, w/o metric prefix replace X 10 6 with corresponding metric prefix, Mega…M convert numerical part to scientific notation There is no metric prefix corresponding to X Change X 10 5 to X Having increased the power of ten by 1, we must compensate by reducing the number by moving the decimal one place to the left.

Alternative Change X 10 5 to X Having decreased the power of ten by 2, we must compensate by increasing the number by moving the decimal two places to the right. replace X 10 3 with corresponding metric prefix, kilo…k

replace X with corresponding metric prefix, micro…  There is no metric prefix corresponding to X Change X to X Having decreased the power of ten by 2, we must compensate by increasing the number by moving the decimal two places to the right. convert numerical part to scientific notation standard decimal, w/o metric prefix

Alternative Change X to X Having increased the power of ten by 1, we must compensate by decreasing the number by moving the decimal one place to the left. replace X with corresponding metric prefix, milli…m

scientific notation w/ metric prefix replace metric prefix (k) with corresponding power of ten… X 10 3 multiply powers of ten by adding exponents Change power of ten from 10 7 to 10 6 and increase the number by moving the decimal one place to the right. Replace X 10 6 with its corresponding metric prefix Mega…M.

replace metric prefix (  ) with corresponding power of ten… X multiply powers of ten by adding exponents Replace X with its corresponding metric prefix nano…n. scientific notation w/ metric prefix

Conversion Factors 1ft = 12in 1yd = 3ft 1mi = 5280ft 1lb = 16oz 1gal = 4qt 1hr = 3600s British Units

Conversion Factors continued Mixed British and Metric Units 1in = 2.54cm 1m = 39.4in 1mi = the earth’s surface 1liter(L) = 1.06qt 1m 3 = 1000L

Unit Conversion Convert 2mi to yds Map: Convert 50cm to inches Map:

Convert.5lb to grams Map: Convert 5yd to cm Map:

Convert 5m 3 to gallons Map:

Therefore, 1 gallon of water weighs 8.3 pounds.

Map: In one year light can travel a distance of 5.9 X miles. This distance of approximately 6 trillion miles is called one light-year and is used by astronomers for measuring the great distances between stars and galaxies.