Video Math Tutor: Basic Math: Lesson 7 - Units Of Measurement
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BASIC MATH A Self-Tutorial by
Luis Anthony Ast Professional Mathematics Tutor
LESSON 7: UNITS OF MEASUREMENT Copyright © 2006 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage or retrieval system, without permission in writing of the author.
E-mail may be sent to: [email protected]
UNITS OF TIME The basic unit of time is the Second, defined as 9,192,631,770 oscillations of the atom of cesium-133.
1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 fortnight = 2 weeks = 14 days (or nights) 1 month
30 days
4 weeks
1 year = 365 days = 52 weeks = 12 months 1 leap year = 366 days 1 decade = 10 years 1 century = 100 years 1 millennium = 1000 years
F ABBREVIATIONS F
2
UNITS OF LENGTH F METRIC SYSTEM F F The Meter is the basic unit of measurement of length. It is defined as the total distance a beam of light would travel in
of a second.
To get an idea of this length, it is approximately equal to just over times the width of a letter size page of paper: Page ===== =====
Page ===== =====
Page ===== =====
Page ===== =====
Page ===== =====
← 1 meter → Assuming the following represents a meter: 1 decimeter =
meter
A better view of this portion is…
1 decimeter
1 centimeter =
decimeter = 3
meter
1 millimeter =
centimeter =
decimeter =
Another look at this:
Keep in mind: 1 meter =
Y Here are units larger than a meter: 1 decameter = 10 meters 1 hectometer = 100 meters
4
meter
F U.S. CUSTOMARY SYSTEM F
=
Imperial Units (United Kingdom) are NOT covered in this lesson, only the American System. Also, not all units are discussed, just the more typical ones. The Yard is the basic unit of measurement of length. It is defined as 0.9144 meters.
1 inch =
foot =
1 foot = 12 inches =
yard
yard
1 yard = 3 feet = 36 inches 1 mile = 1760 yards = 5280 feet
F CONVERSIONS F Here are the most typical formulas to convert units from one system to another. Most values are approximate, unless otherwise noted. I will provide one example of how to use them. This is meant more as a reference. More manipulations of units are done in other Lessons. 0.393701 × centimeters = inches 2.54 × inches = centimeters <exactly> 3.28084 × meters = feet 0.3048 × feet = meters <exactly>
5
1.093613 × meters = yards 0.9144 × yards = meters <exactly> 0.621371 × kilometers = miles 1.609344 × miles = kilometers <exactly>
F ABBREVIATIONS F
EXAMPLE 1: Convert 38 inches into centimeters. SOLUTION: To convert inches to centimeters, we will use the formula: 2.54 × inches = centimeters 2.54 × 38 = 96.52 The Answer is 96.52cm.
6
UNITS OF AREA F METRIC SYSTEM F F The Square Meter is the basic unit of measurement of area. It is defined as a square whose sides are of length one meter.
1 meter
← 1 meter → ← 1 square millimeter =
square centimeter
← 1 square centimeter =
square decimeter
1 square decimeter = 7
square meter
Y Other units: 1 square decameter = 100 square meters 1 square hectometer = 100 square decameters 1 square kilometer = 100 square hectometers
F U.S. CUSTOMARY SYSTEM F F The Square Yard is the basic unit of measurement of area. It is defined as a square whose sides are of length one yard.
1 yard
← 1 yard
→
← 1 square inch
1 square inch ↓
← 1 square foot = 144 square inches
1 square foot ↓
← 1 square yard = 9 square feet = 1296 square inches
8
1 = 4840 square yards acre 1 square mile = 640 acres
F CONVERSIONS F 0.155 × square centimeters = square inches 6.4516 × square inches = square centimeters <exactly> 10.76391 × square meters = square feet 0.092903 × square feet = square meters 1.19599 × square meters = square yards 0.836127 × square yards = square meters 0.3861 × square kilometers = square miles 2.590 × square miles = square kilometers
F ABBREVIATIONS F
9
UNITS OF VOLUME F METRIC SYSTEM F F The Cubic Meter is the basic unit of measurement of volume. It is defined as a cube whose sides are of length one meter.
1 meter
←1 meter→ "←
1 cubic millimeter =
1 meter
cubic centimeter
← 1 cubic centimeter =
1 cubic decimeter =
cubic decimeter
cubic meter 10
Y Other units: 1 cubic decameter = 1000 cubic meters 1 cubic hectometer = 1000 cubic decameters 1 cubic kilometer = 1000 cubic hectometers
F U.S. CUSTOMARY SYSTEM F F The Cubic Yard is the basic unit of measurement of volume. It is defined as a cube whose sides are of length one yard.
1 yard
←1 yard →
← 1 cubic inch =
1 yard
cubic foot
1 cubic foot = 1728 cubic inches =
cubic yard
7.481 gallons
1 cubic yard = 27 cubic feet
4 feet
1 cord = 4 × 4 × 8 feet = 128 cubic feet
8 feet ←4
feet→
11
F CONVERSIONS F 0.061024 × cubic centimeters = cubic inches 16.387064 × cubic inches = cubic centimeters <exactly> 35.314667 × cubic meters = cubic feet 0.028317 × cubic feet = cubic meters 1.307951 × cubic meters = cubic yards 0.764555 × cubic yards = cubic meters
F ABBREVIATIONS F
12
UNITS OF MASS F METRIC SYSTEM F The Kilogram is the basic unit of measurement of mass. It is defined as the mass of a certain cylinder made of platinum–iridium kept in Sèvres, France. It is called the International Prototype Kilogram. [
1 milligram = 1 gram =
gram kilogram
1 kilogram = 1000 grams
1 metric ton = 1000 kilograms = How I usually feel after a big lunch!
F U.S. CUSTOMARY SYSTEM F The Pound is the basic unit of measurement of mass. It is defined to be 0.45359237 kilograms. <Exactly>
1 ounce =
pound
1 pound = 16 ounces 1 ton = 2000 pounds
13
F CONVERSIONS F 0.035274 × grams = ounces 28.349523 × ounces = grams 2.204623 × kilograms = pounds 0.45359237 × pounds = kilograms <exactly> 0.9071874 × short tons = metric tons 1.102312 × metric tons = short tons
F ABBREVIATIONS F
ounce = oz pound = lb
14
UNITS OF LIQUID CAPACITY F METRIC SYSTEM F The Liter is the basic unit of measurement of capacity (both liquid and dry). It is the volume of 1 kilogram of water under specific scientific conditions. 1 milliliter =
liter = 1 cubic centimeter
1 liter = 1000 milliliters = 1 cubic decimeter
1 kiloliter = 1000 liters = 1 cubic meter
F U.S. CUSTOMARY SYSTEM F F The Gallon is the basic unit of measurement of liquid capacity. It is equal to 231 cubic inches. 1 drop =
teaspoon =
1 teaspoon =
fluid ounce
tablespoon = 60 drops = fluid ounce
1 tablespoon = 3 teaspoons = 15
fluid ounce =
cup
1 fluid ounce =
pint =
quart =
1 cup =
pint = 8 fluid ounces
1 pint =
quart = 16 fluid ounces
1 quart =
gallon
gallon = 2 pints = 4 cups = 32 fluid ounces
1 gallon = 4 quarts = 128 fluid ounces
F CONVERSIONS F 0.264172 × liters = gallons 3.785411784 × gallons = liters <exactly> 1.056688 × liters = quarts 0.946353 × quarts = liters
F ABBREVIATIONS F
16
UNITS OF DRY CAPACITY F METRIC SYSTEM F Same as liquid.
F U.S. CUSTOMARY SYSTEM F F The Bushel is the basic unit of measurement of dry capacity. It is equal to 2150.42 cubic inches.
=
Although the same names are used, liquid pints and quarts are NOT the same size as dry pints and quarts. 1 pint =
quart
1 quart = 2 pints = 1 peck = 8 quarts =
peck bushel
1 bushel = 4 pecks
F CONVERSIONS F 1.816166 × liters = dry pints 0.550610 × dry pints = liters 0.908083 × liters = dry quarts 1.101221 × dry quarts = liters 0.113510 × liters = pecks 8.809768 × pecks = liters 0.028378 × liters = bushels 35.23907016688 × bushels = liters <exactly> 17
F ABBREVIATIONS F
OTHER USEFUL INFORMATION F SOME COUNTING UNITS F 1 dozen = 12 (Abbreviation: dz) 1 baker’s dozen = 13 1 score = 20 1 gross = 144 (12 dozens) (Abbreviation: gr) 1 ream = 500 (Abbreviation: rm)
F ANGLE MEASURE F 1 second =
minute
1 minute =
degree
1 degree =
of a circle
SYMBOLS: Degree: °
Minute: ′
Second: ″
← 1 degree = 1°
18
← 1 right angle = 90° =
of a circle
← 1 straight angle = 180° =
A protractor is typically used to measure angles:
19
of a circle
F UNITS OF TEMPERATURE F F The Degree is used as the basic unit of temperature; however, there are several temperature scales commonly used. Two will be discussed here: Fahrenheit and Celsius. Math Symbol: F
Degrees Fahrenheit:
← Boiling point of water
212°F→
180 degrees 32°F→
← Freezing point of water
Math Symbol: C
Degrees Celsius:
← Boiling point of water
100°C→
100 degrees 0°C→
← Freezing point of water
20
Y If you are given degrees Celsius (C) and want degrees Fahrenheit (F), use this formula to convert the values:
Y If you are given degrees Fahrenheit (F) and want degrees Celsius (C), use this formula to convert the values:
Examples of these conversions will be done in another Lesson.
END OF LESSON 7 21
Luis Anthony Ast Professional Mathematics Tutor
LESSON 7: UNITS OF MEASUREMENT Copyright © 2006 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage or retrieval system, without permission in writing of the author.
E-mail may be sent to: [email protected]
UNITS OF TIME The basic unit of time is the Second, defined as 9,192,631,770 oscillations of the atom of cesium-133.
1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 fortnight = 2 weeks = 14 days (or nights) 1 month
30 days
4 weeks
1 year = 365 days = 52 weeks = 12 months 1 leap year = 366 days 1 decade = 10 years 1 century = 100 years 1 millennium = 1000 years
F ABBREVIATIONS F
2
UNITS OF LENGTH F METRIC SYSTEM F F The Meter is the basic unit of measurement of length. It is defined as the total distance a beam of light would travel in
of a second.
To get an idea of this length, it is approximately equal to just over times the width of a letter size page of paper: Page ===== =====
Page ===== =====
Page ===== =====
Page ===== =====
Page ===== =====
← 1 meter → Assuming the following represents a meter: 1 decimeter =
meter
A better view of this portion is…
1 decimeter
1 centimeter =
decimeter = 3
meter
1 millimeter =
centimeter =
decimeter =
Another look at this:
Keep in mind: 1 meter =
Y Here are units larger than a meter: 1 decameter = 10 meters 1 hectometer = 100 meters
4
meter
F U.S. CUSTOMARY SYSTEM F
=
Imperial Units (United Kingdom) are NOT covered in this lesson, only the American System. Also, not all units are discussed, just the more typical ones. The Yard is the basic unit of measurement of length. It is defined as 0.9144 meters.
1 inch =
foot =
1 foot = 12 inches =
yard
yard
1 yard = 3 feet = 36 inches 1 mile = 1760 yards = 5280 feet
F CONVERSIONS F Here are the most typical formulas to convert units from one system to another. Most values are approximate, unless otherwise noted. I will provide one example of how to use them. This is meant more as a reference. More manipulations of units are done in other Lessons. 0.393701 × centimeters = inches 2.54 × inches = centimeters <exactly> 3.28084 × meters = feet 0.3048 × feet = meters <exactly>
5
1.093613 × meters = yards 0.9144 × yards = meters <exactly> 0.621371 × kilometers = miles 1.609344 × miles = kilometers <exactly>
F ABBREVIATIONS F
EXAMPLE 1: Convert 38 inches into centimeters. SOLUTION: To convert inches to centimeters, we will use the formula: 2.54 × inches = centimeters 2.54 × 38 = 96.52 The Answer is 96.52cm.
6
UNITS OF AREA F METRIC SYSTEM F F The Square Meter is the basic unit of measurement of area. It is defined as a square whose sides are of length one meter.
1 meter
← 1 meter → ← 1 square millimeter =
square centimeter
← 1 square centimeter =
square decimeter
1 square decimeter = 7
square meter
Y Other units: 1 square decameter = 100 square meters 1 square hectometer = 100 square decameters 1 square kilometer = 100 square hectometers
F U.S. CUSTOMARY SYSTEM F F The Square Yard is the basic unit of measurement of area. It is defined as a square whose sides are of length one yard.
1 yard
← 1 yard
→
← 1 square inch
1 square inch ↓
← 1 square foot = 144 square inches
1 square foot ↓
← 1 square yard = 9 square feet = 1296 square inches
8
1 = 4840 square yards acre 1 square mile = 640 acres
F CONVERSIONS F 0.155 × square centimeters = square inches 6.4516 × square inches = square centimeters <exactly> 10.76391 × square meters = square feet 0.092903 × square feet = square meters 1.19599 × square meters = square yards 0.836127 × square yards = square meters 0.3861 × square kilometers = square miles 2.590 × square miles = square kilometers
F ABBREVIATIONS F
9
UNITS OF VOLUME F METRIC SYSTEM F F The Cubic Meter is the basic unit of measurement of volume. It is defined as a cube whose sides are of length one meter.
1 meter
←1 meter→ "←
1 cubic millimeter =
1 meter
cubic centimeter
← 1 cubic centimeter =
1 cubic decimeter =
cubic decimeter
cubic meter 10
Y Other units: 1 cubic decameter = 1000 cubic meters 1 cubic hectometer = 1000 cubic decameters 1 cubic kilometer = 1000 cubic hectometers
F U.S. CUSTOMARY SYSTEM F F The Cubic Yard is the basic unit of measurement of volume. It is defined as a cube whose sides are of length one yard.
1 yard
←1 yard →
← 1 cubic inch =
1 yard
cubic foot
1 cubic foot = 1728 cubic inches =
cubic yard
7.481 gallons
1 cubic yard = 27 cubic feet
4 feet
1 cord = 4 × 4 × 8 feet = 128 cubic feet
8 feet ←4
feet→
11
F CONVERSIONS F 0.061024 × cubic centimeters = cubic inches 16.387064 × cubic inches = cubic centimeters <exactly> 35.314667 × cubic meters = cubic feet 0.028317 × cubic feet = cubic meters 1.307951 × cubic meters = cubic yards 0.764555 × cubic yards = cubic meters
F ABBREVIATIONS F
12
UNITS OF MASS F METRIC SYSTEM F The Kilogram is the basic unit of measurement of mass. It is defined as the mass of a certain cylinder made of platinum–iridium kept in Sèvres, France. It is called the International Prototype Kilogram. [
1 milligram = 1 gram =
gram kilogram
1 kilogram = 1000 grams
1 metric ton = 1000 kilograms = How I usually feel after a big lunch!
F U.S. CUSTOMARY SYSTEM F The Pound is the basic unit of measurement of mass. It is defined to be 0.45359237 kilograms. <Exactly>
1 ounce =
pound
1 pound = 16 ounces 1 ton = 2000 pounds
13
F CONVERSIONS F 0.035274 × grams = ounces 28.349523 × ounces = grams 2.204623 × kilograms = pounds 0.45359237 × pounds = kilograms <exactly> 0.9071874 × short tons = metric tons 1.102312 × metric tons = short tons
F ABBREVIATIONS F
ounce = oz pound = lb
14
UNITS OF LIQUID CAPACITY F METRIC SYSTEM F The Liter is the basic unit of measurement of capacity (both liquid and dry). It is the volume of 1 kilogram of water under specific scientific conditions. 1 milliliter =
liter = 1 cubic centimeter
1 liter = 1000 milliliters = 1 cubic decimeter
1 kiloliter = 1000 liters = 1 cubic meter
F U.S. CUSTOMARY SYSTEM F F The Gallon is the basic unit of measurement of liquid capacity. It is equal to 231 cubic inches. 1 drop =
teaspoon =
1 teaspoon =
fluid ounce
tablespoon = 60 drops = fluid ounce
1 tablespoon = 3 teaspoons = 15
fluid ounce =
cup
1 fluid ounce =
pint =
quart =
1 cup =
pint = 8 fluid ounces
1 pint =
quart = 16 fluid ounces
1 quart =
gallon
gallon = 2 pints = 4 cups = 32 fluid ounces
1 gallon = 4 quarts = 128 fluid ounces
F CONVERSIONS F 0.264172 × liters = gallons 3.785411784 × gallons = liters <exactly> 1.056688 × liters = quarts 0.946353 × quarts = liters
F ABBREVIATIONS F
16
UNITS OF DRY CAPACITY F METRIC SYSTEM F Same as liquid.
F U.S. CUSTOMARY SYSTEM F F The Bushel is the basic unit of measurement of dry capacity. It is equal to 2150.42 cubic inches.
=
Although the same names are used, liquid pints and quarts are NOT the same size as dry pints and quarts. 1 pint =
quart
1 quart = 2 pints = 1 peck = 8 quarts =
peck bushel
1 bushel = 4 pecks
F CONVERSIONS F 1.816166 × liters = dry pints 0.550610 × dry pints = liters 0.908083 × liters = dry quarts 1.101221 × dry quarts = liters 0.113510 × liters = pecks 8.809768 × pecks = liters 0.028378 × liters = bushels 35.23907016688 × bushels = liters <exactly> 17
F ABBREVIATIONS F
OTHER USEFUL INFORMATION F SOME COUNTING UNITS F 1 dozen = 12 (Abbreviation: dz) 1 baker’s dozen = 13 1 score = 20 1 gross = 144 (12 dozens) (Abbreviation: gr) 1 ream = 500 (Abbreviation: rm)
F ANGLE MEASURE F 1 second =
minute
1 minute =
degree
1 degree =
of a circle
SYMBOLS: Degree: °
Minute: ′
Second: ″
← 1 degree = 1°
18
← 1 right angle = 90° =
of a circle
← 1 straight angle = 180° =
A protractor is typically used to measure angles:
19
of a circle
F UNITS OF TEMPERATURE F F The Degree is used as the basic unit of temperature; however, there are several temperature scales commonly used. Two will be discussed here: Fahrenheit and Celsius. Math Symbol: F
Degrees Fahrenheit:
← Boiling point of water
212°F→
180 degrees 32°F→
← Freezing point of water
Math Symbol: C
Degrees Celsius:
← Boiling point of water
100°C→
100 degrees 0°C→
← Freezing point of water
20
Y If you are given degrees Celsius (C) and want degrees Fahrenheit (F), use this formula to convert the values:
Y If you are given degrees Fahrenheit (F) and want degrees Celsius (C), use this formula to convert the values:
Examples of these conversions will be done in another Lesson.
END OF LESSON 7 21
