Download - Units & Measurement
Measurement
You are making a measurement when you Check you weight Read your watch Take your temperature Weigh a watermelon
What kinds of measurements did you make today?
Why 12 inches not 10 or 13?
Simply because it took 12 lengths of his first knuckle to
equal his foot.
...So they used the length of the King’s first knuckle
One InchBut that was too big for some
other things...
You should have noticed that as the fractions got
smaller, so did the length of the lines between the
whole numbers. That helps to identify a half from the fourths and so
on.
If you don’t remember what the fraction is just by looking at the ruler,
you can always count the number of lines between
the whole numbers. If there are 16, then your
ruler is divided into sixteenths.
..then you can do the math to determine the fraction.
If you counted 10 lines from the whole number, that would be 10 sixteenths. Here’s where that
“magic number 2” comes in.To get the fraction to it’s lowest possible
denominator DIVIDE both numbers in the fraction by 2 and keep doing it until the top number is odd.
10 = 5 Top number’s odd so 10/16 = 5/816 8
If the fraction comes between two whole numbers like 1 and 2, then the measurement is the first whole number and the fraction in this case it
would be 1 and 5/8ths
The Metric ruler is much different. Everything is
based on 10
10mm (millimeters) = 1cm (centimeter)100cm= 1m (meter)
1m = 100cm (cm = centimeter, cent means 100)
1m = 1000mm (mm = millimeter, mil means 1000)
English Base Units
• For measuring length a yard is used and one yard = 0.914 meters
• An inch is used for measuring the length of smaller objects and 1inch = 2.54 cm
• An ounce is used for measuring the mass of smaller objects and 1 ounce = 28.35 grams.
English Base Units
• A fluid ounce (oz.) is used to measure the volume of smaller objects and 1 fluid ounce = 29.6 milliliters
English Base Units
Metric System• The metric system is based on a base
unit that corresponds to a certain kind of measurement
• Length = meter• Volume = liter• Weight (Mass) = gram
• Prefixes plus base units make up the metric system – Example:
• Centi + meter = Centimeter• Kilo + liter = Kiloliter
Metric System• The three prefixes that we will use
the most are:– kilo– centi– milli
kilo hecto deca
Base Unitsmetergramliter
deci centi milli
Metric System• So if you needed to measure
length you would choose meter as your base unit– Length of a tree branch
• 1.5 meters – Length of a room
• 5 meters – Length of a ball of twine stretched out
• 25 meters
Metric System• But what if you need to measure a
longer distance, like from your house to school?– Let’s say you live approximately 10
miles from school• 10 miles = 16093 meters
– 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage:• 16093 meters = 16.093 kilometers (or
16.1 if rounded to 1 decimal place)
Metric System• These prefixes are based on powers of
10. What does this mean?– From each prefix every “step” is either:
• 10 times larger or
• 10 times smaller– For example
• Centimeters are 10 times larger than millimeters• 1 centimeter = 10 millimeters
kilo hecto deca
Base Unitsmetergramliter
deci centi milli
Metric System– Centimeters are 10 times
larger than millimeters so it takes more millimeters for the same length
1 centimeter = 10 millimetersExample not to scale
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 cm
40
41
41
40
Metric System• For each “step” to right,
you are multiplying by 10• For example, let’s go from a base unit to centi
1 liter = 10 deciliters = 100 centiliters
2 grams = 20 decigrams = 200 centigrams
kilo hecto decameterliter
gramdeci centi milli
( 1 x 10 = 10) = (10 x 10 = 100)
(2 x 10 = 20) = (20 x 10 = 200)
Metric System• An easy way to move within the metric
system is by moving the decimal point one place for each “step” desiredExample: change meters to centimeters
1 meter = 10 decimeters = 100 centimetersor1.00 meter = 10.0 decimeters = 100. centimeters
kilo hecto decameterliter
gramdeci centi milli
Metric System• Now let’s try our previous example from
meters to kilometers:16093 meters = 1609.3 decameters = 160.93
hectometers = 16.093 kilometers• So for every “step” from the base unit to kilo,
we moved the decimal 1 place to the left (the same direction as in the diagram below)
kilo hecto decameterliter
gramdeci centi milli
Metric System• If you move to the left in the diagram,
move the decimal to the left
• If you move to the right in the diagram, move the decimal to the right
kilo hecto decameterliter
gramdeci centi milli
Metric System• Now let’s start from centimeters and
convert to kilometers
400000 centimeters = 4 kilometers
400000 centimeters = 4.00000 kilometers
kilo hecto decameterliter
gramdeci centi milli
Metric System• Now let’s start from meters and convert to
kilometers
4000 meters = 4 kilometerskilo hecto deca
meterliter
gramdeci centi milli
kilo hecto decameterliter
gramdeci centi milli
• Now let’s start from centimeters and convert to meters
4000 centimeters = 40 meters
Metric System• Now let’s start from meters and convert to
centimeters
5 meters = 500 centimeterskilo hecto deca
meterliter
gramdeci centi milli
kilo hecto decameterliter
gramdeci centi milli
• Now let’s start from kilometers and convert to meters
.3 kilometers = 300 meters
Metric System• Now let’s start from kilometers and convert
to millimeters
4 kilometers = 4000000 millimetersor
4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = 400000 centimeters = 4000000 millimeters
kilo hecto decameterliter
gramdeci centi milli
Metric System• Summary
– Base units in the metric system are meter, liter, gram
– Metric system is based on powers of 10– For conversions within the metric system, each
“step” is 1 decimal place to the right or left– Using the diagram below, converting to the right,
moves the decimal to the right and vice versa
kilo hecto decameterliter
gramdeci centi milli
Systems of Measurement• Why do we need a standardized system of
measurement?– Scientific community is global.– An international “language” of measurement allows
scientists to share, interpret, and compare experimental findings with other scientists, regardless of nationality or language barriers.
• By the 1700s, every country used its own system of weights and measures. England had three different systems just within its own borders!
Metric System & SI• The first standardized system of measurement:
the “Metric” system– Developed in France in 1791– Named based on French word for “measure”– based on the decimal (powers of 10)
• Systeme International d'Unites(International System of Units)– Modernized version of the Metric System– Abbreviated by the letters SI.– Established in 1960, at the 11th General Conference
on Weights and Measures.– Units, definitions, and symbols were revised and
simplified.
UNIT CONVERSIONS• Quantities can be converted from one
type of unit to another. This conversion may occur within the same system (metric or English) or between systems (metric to English or English to metric).
• Conversions cannot be made between measures of different properties, that is, mass units to length units for example.
• A method of unit conversion commonly used is called Dimensional Analysis or Unit Analysis. In this procedure, units are used to decide when to multiply or divide in order to obtain the correct answer.
Dimensional/ Unit Analysis – metric to metric
1. How many meters are contained in 800cm?
800 cm m
800 cm x 1 m = 800 = 8 m 100 cm 100
2. How many Kg are there in 1200 g?
1200g Kg1200 g x 1Kg = 1200 = 1.2 Kg 1000 g 1000
Dimensional/Unit Analysis – English metric
1. How many grams are contained in 25 lbs?
25 lbs g 25 lbs x 1Kg x 1000g = 25 000
2.2 lbs 1 Kg 2.2
=11 363.63 g
2. How many pounds are there in 75 Kg?75Kg lbs75 Kg x 2.2 lbs = 165 lbs
1 Kg
* How many minutes are there in 2 days and 6 hours?
2 days, 6 hrs mins2 days x 24 hrs = 48 hrs + 6 hrs = 54 hrs 1 day
54 hrs x 60 mins = 3 240 mins 1 hr