Measurement

Measurement is the process of assigning numbers to quantities 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 kind of measurements did you make today?

Measurement Basics Length: is the distance of something measured Volume/Capacity: how much something can hold ( generally liquid); how much space something takes up Mass: amount of matter in an object

US/Customary System/English System The US/Customary system has many different units of measurement Each unit has a completely different name They also have completely different conversion factors

Metric System The metric system has base unit and many different prefixes

Metric Units of Measurement Meters: Measures length Liters: Measures volume or capacity Grams: measures mass

Units of Measurement: Volume US System Cups Pints Quarts Gallons Fluid Ounces Metric System Liters

Units of Measurement: Length US System Inches Feet Yards Miles Metric Meters

Units of Measurement: Weight/Mass US System Ounce Pound Tons Metric Gram

Metric System Prefixes Mili- 1/1000, which means that 1000mm=1m Centi- 1/100, which means that 100cg=1g Deci- 1/10, which means that 10dl=1l Deka- 10, which means that 1dkm=10m Hecto- 100, which means that 1hg=100g Kilo- 1000, which means that 1kl=1000l

US Conversions Length 1 foot = 12 inches 1 yard = 3 feet 1 mile = 5,280 feet

US Conversions Volume 1 cup = 8 fl oz 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts

US Conversions Weight 1 lb = 16 oz 1 ton = 2000 lbs

Measuring Distance in English Using a measuring tool called a ruler

Where did it come from? Why 12 inches?

The King’s Foot One Foot Although no single document on the subject can be found, it appears that during the reign of Henry I (1100-1135) the 12-inch foot became official, and the royal government took steps to make this foot length known. A 12-inch foot was inscribed on the base of a column of St. Paul's Church in London, and measurements in this unit were said to be "by the foot of St. Paul's" (de pedibus Sancti Pauli). Henry I also appears to have ordered construction of 3-foot standards, which were called "yards," thus establishing that unit for the first time in England. William of Malmsebury wrote that the yard was "the measure of his [the king's] own arm," thus launching the story that the yard was defined to be the distance from the nose to the fingertip of Henry I. Have three students (choose by foot size – one small, one avg and one large) Have them start by aligning their heels side by side and make 10 paces straight ahead. They should not stop at the same distance. Tell the kids that this proves that measuring this way is not efficient. A better way to measure was needed, thus the ruler was invented.

The King’s Foot One Foot Too 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 Inch But that was too big for some other things...

...That’s exactly how they made the fractions between the inches. 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, 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 = 5/8 16 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 Go back to the ruler slide and continue to point at various fractions

Name this measurement 1/2 1/3 1/4 5/16

Name this measurement 3/4 3/8 1-3/4 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

Here’s a meter stick!

It takes 10 decimeters to make up 1 meter.

It takes 10 centimeters to make up 1 decimeter.

If 1 meter = 10 decimeters and 1 decimeter = 10 centimeters then how many centimeters make up 1 meter?

That’s right! 1 meter = 100 centimeters

100centimeters = 1 meter

It takes 10 millimeters to make up 1 centimeter.

If 1 meter = 10 decimeters and 1 decimeter = 10 centimeters and 1centimeter = 10 millimeters then how many millimeters make up 1 meter?

That’s right! 1000 millimeters = 1 meter

It takes 10 millimeters to make up 1 centimeter. Millimeters are so small that they almost run together.

Now let’s take a closer look at some measuring devices.

This is a magnified image of a ruler/meter stick. 1 2 3 4 This is one centimeter.

This is a magnified image of a ruler/meter stick. 1 2 3 4 This is half of a centimeter.

This is a magnified image of a ruler/meter stick. 1 2 3 4 This is one millimeter.

This key measures 3 cm. 1 2 3 4

Or you could say that it measures 30 mm. 1 2 3 4

This key measures 2.5 cm. 1 2 3 4

Or, you could say that it measures 25 mm. 1 2 3 4

1 2 3 4 This toy car measures 4.2 cm.

Or, you could say it measures 42 mm. 1 2 3 4 Or, you could say it measures 42 mm.

The metric system deals with powers of 10 1 meter = 10 decimeters = 100 centimeters = 1000 millimeters