Units & Measurement

•Measurement is the process of assigning numbers to quantities. It involves a quantity and a unit.

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?

Where did it come from?

Why 12 inches?

The King’s Foot

One Foot

The King’s Foot

One FootToo big for some

things...

...So they used the length of the King’s first knuckle

One Inch

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...

...That’s exactly how they made inches. the fractions between the

1/2 1/4

...So they cut the inches into fractions

1/2 1/4 1/8 and 1/16

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

Name this measurement

A. A. 1/2B. B. 1/3C. C. 1/4D. D. 5/16

Name this measurement

A. A. 3/4B. B. 3/8C. C. 1-3/4D. D. 2-3/4

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)

The Metric Ruler

This is a magnified image of a

ruler/meter stick.

1

This is half of a centimeter.

2 3 4

This is a magnified image of a

ruler/meter stick.

1

This is one millimeter.

2 3 4

TWO SYSTEMS OF

MEASUREMENT

ENGLISH SYSTEM

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

English Base Units• For measuring mass the pound is

used and one pound = 0.45 kilograms

• An ounce is used for measuring the mass of smaller objects and 1 ounce = 28.35 grams.

English Base Units

English Base Units

• For measuring volume a gallon is used and 1 gallon = 3.78 liters

• A fluid ounce (oz.) is used to measure the volume of smaller objects and 1 fluid ounce = 29.6 milliliters

English Base Units

Metric Syste

m

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



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)



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



Metric System• Now let’s start from centimeters and

convert to kilometers

400000 centimeters = 4 kilometers

400000 centimeters = 4.00000 kilometers



Metric System• Now let’s start from meters and convert to

kilometers

4000 meters = 4 kilometerskilo hecto deca

meterliter




• 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




• 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



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



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.

FROM THE CONVERSION TABLE

Perform the operations

CANCEL UNITS TO LEAVE UNITS OF THE 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 seconds are there in 90 minutes?

90 mins secs90 mins x 60 secs = 5400 secs 1 min

* 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

Convert the following using Dimensional

Analysis• 1) 950 g Kg• 2) 112 lbs g• 3) 25 L ml• 4) 3.5Km m• 5) 2 days & 3 hours min

Units & Measurement

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