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Metric system

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American still often use the “traditional systems of weights and measures”. It was developed from English units, used by the British Empire before American independence.

The British system of measures was overhauled in 1824 to create the Imperial system, changing the definitions of some units. So while many U.S. units are similar to their Imperial counterparts, there are now some differences between the systems.

Why didn’t we change to the Metric system, like the rest of the world?

Some common conversion factors:

Conversions

Metric table 1
Metric table 2

1. Why do Americans use the English/Imperial system instead of the Metric system?

2. Why do we (sometimes) need to convert between Metric and English?

3. What’s the big deal? Come up with 2 examples of things that could go very, very wrong, if someone mixes up metric and English units:

Simpsons Metric system is the tool of the Devil

4. Show me that you know the English system

Copy this into your notes, and fill in the blanks: But don’t look the answers up: We’re testing to see if we really, truly know the English system!

1 inch (in.) = _____ feet

1 foot = __________ inches

1 foot (ft) = ____ yard

1 yard = ____ feet

1 rod (rd) = ____  yards

1 furlong = ____  yards =  _____ mile

1 mile = ______ yards = ______ feet

1 nautical mile = _____ feet

1 acre = _____________ square feet

1 tablespoon = ___________ teaspoons

1 US fluid ounce (fl oz) = _____ tabelspoons

1 pint = ________ cups

1 barrel = __________ gallons

1 hogshead = ________ gallons

1 pound = ________ ounces

1 long hundredweight = ____ pounds

1 ton = ___ pounds

Some solutions

1 inch (in.) = 1/36 yard = 1/12 foot
1 foot = 12 inches
1 foot (ft) = 1/3 yard
1 yard (yd) = 3 feet
1 rod (rd) = 5 ½ yards
1 furlong = 220 yards = 1/8 mile
1 mile = 1,760 yards = 5,280 feet
1 fathom = 6 feet
1 nautical mile = 6,076.1 feet

america rejects metric system King Henry's foot

Area

Unit Divisions SI Equivalent

Exact relationships shown in boldface

1 square survey foot (sq ft or ft2)

144 square inches

0.09290341 m2

1 square chain (sq ch or ch2)

4356 sq ft (survey) or 16 sq rods

404.6873 m2

1 acre

43560 sq ft (survey) or 10 sq ch

4046.873 m2

1 section

640 acres or 1 sq mile (survey)

2.589998 km2

1 survey township (twp)

36 sections or 4 sq leagues

93.23993 km2

Volume

Volume in general

Unit

Divisions

SI Equivalent

1 cubic inch (cu in) or (in3)

16.387064 mL[13]

1 cubic foot (cu ft) or (ft3)

1728 cu in

28.31685 L

1 cubic yard (cu yd) or (yd3)

27 cu ft

764.554857984 L

0.764554857984 m3

1 acre-foot (acre ft)

43560 cu ft

1613.333 cu yd

1.233482 ML

1233.482 m3

Unit Divisions SI Equivalent

1 minim (min)

~1 drop or 0.95 grain of water

61.611519921875 μL

1 US fluid dram (fl dr)

60 min

3.6966911953125 mL

1 teaspoon (tsp)

80 min

4.92892159375 mL

1 tablespoon (Tbsp)

3 tsp or 4 fl dr

14.78676478125 mL

1 US fluid ounce (fl oz)

2 Tbsp or 1.0408 oz av of water

29.5735295625 mL

1 US shot (jig)

3 Tbsp

44.36029434375 mL

1 US gill (gi)

4 fl oz

118.29411825 mL

1 US cup (cp)

2 gi or 8 fl oz

236.5882365 mL

1 (liquid) US pint (pt)

2 cp or 16.65 oz av of water

473.176473 mL

1 (liquid) US quart (qt)

2 pt

0.946352946 L

1 (liquid) US gallon (gal)

4 qt or 231 cu in

3.785411784 L

1 (liquid) barrel (bbl)

31.5 gal or 12 hogshead

119.240471196 L

1 oil barrel (bbl)

42 gal or 23 hogshead

158.987294928 L

1 hogshead

63 gal or 8.421875 cu ft

or 524.7 lb of water

238.480942392 L

Units of Mass

Conversions

Type

Unit

Divisions

SI equivalent

Avoirdupois

1 grain (gr)

17000 lb

64.79891 mg

1 dram (dr)

27 1132 gr or 8.859 carats

1.7718451953125 g

1 ounce (oz)

16 dr

28.349523125 g

1 pound (lb)

16 oz

453.59237 g

1 US hundredweight (cwt)

100 lb

45.359237 kg

1 long hundredweight

112 lb

50.80234544 kg

1 ton (short ton)

20 US cwt or 2000 lb

907.18474 kg

1 long ton

20 long cwt or 2240 lb

1016.0469088 kg

Troy

1 grain (gr)

17000 lb av or 15760 lb t

64.79891 mg

1 pennyweight (dwt)

24 gr or 7.776 carats

1.55517384 g

1 troy ounce (oz t)

20 dwt

31.1034768 g

1 troy pound (lb t)

12 oz t or 13.17 oz av

373.2417216 g

Most common measures shown in italics
Exact conversions shown in bold

5. We need the metric system to simplify this

Presentation on the Metric system

6. How to do Metric conversions

To convert from a smaller unit to a larger unit:

Count the number of lines up the table; move the decimal this many spaces left.

______________________________________________________

The Joker and the metric system

To convert from a larger unit to a smaller unit:

Count the number of lines down the table; move the decimal this many spaces right.

metric system table

metric system table

Palpatine Let the Metric System Flow Through You

To convert from a smaller unit to a larger unit:

1,000 grams is how many kilograms?

Kilo is three lines up; move the decimal point three spaces to the left

1,000 ⇨ 1.000 1,000 grams is the same as 1 kilogram
_________________________________________________

1,000 meters is how many kilometers?

Kilo is three lines up; move the decimal point three spaces to the left

1,000 ⇨ 1.000 1,000 m is the same as 1 km

_________________________________________________

1,000 liters is how many kiloliters?

Kilo is three lines up; move the decimal point three spaces to the left

1,000 ⇨ 1.000 1,000 liters is the same as 1 kiloliter

_________________________________________________
Wow! Conversions are the same in grams, meters, liters, degrees, or any other units!
_________________________________________________

1,000 μg micrograms is how many decigrams?

Deci is five lines up; move the decimal five spaces to the left.

1,000 ⇨ 0.01 1,000 μg is the same as 0.01 decigrams

_________________________________________________

25,000 microliters (also: 25,000 μL) is how many liters?

Liters has no prefix; it is the base unit line. This line is six lines up.

Move the decimal six places left.

25,000 ⇨ 0.025 liters 25,000 μL is 0.025 L

_________________________________________________

520,000 millimeters is how many kilometers?

Kilo is six lines up; move the decimal six spaces left.

520,000 mm ⇨ 0.52 km 520,000 mm is 0. 52 km

_________________________________________________

To convert from a larger unit to a smaller unit:

1,000 grams is how many milligrams?

Milli is three lines down; move the decimal point three spaces to the right.

1,000 ⇨ 1,000,000 1,000 g is 1,000,000 mg

_________________________________________________

0.05 megabytes is how many kilobytes?

Kilo is three lines down; move the decimal point three spaces right.

0.05 ⇨ 50 0.05 megabytes is 50 kilobytes

_________________________________________________

1 dekagram is how many micrograms?

Micro is seven lines down; move the decimal point seven spaces right.

1 ⇨ 1,000,000 1 dg is 10,000,000 μg

7. Converting from one system to another.

Sometimes we’ll need to convert from one system to another, for example from metric to Imperial (English.) To do that we’ll use dimensional analysis.

Dimensional analysis: KaiserScience

_________________________________________________

Learning standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Science and Engineering Practices: 5. Using Mathematics and Computational Thinking:
Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m 3, acre-feet, etc.).

National Council of Teachers of Mathematics
Students need to develop an understanding of metric units and their relationships, as well as fluency in applying the metric system to real-world situations. Because some non-metric units of measure are common in particular contexts, students need to develop familiarity with multiple systems of measure, including metric and customary systems and their relationships.

National Science Teachers Association
The efficiency and effectiveness of the metric system has long been evident to scientists, engineers, and educators. Because the metric system is used in all industrial nations except the United States, it is the position of the National Science Teachers Association that the International

Metric system tutorial
http://www.chemistryland.com/CHM151W/01-Foundation/Metric/Metrics151.html

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