video math tutor: basic math: lesson 7 - units of measurement

B A S I C M A T H A Self-Tutorial

by

Luis Anthony AstProfessional Mathematics Tutor

LESSON 7:

UNITS OF MEASUREMENT

Copyright © 2006

All rights reserved. No part of this publication may be reproduced or transmitted in any formor by any means, electronic or mechanical, including photocopy, recording, or any informationstorage or retrieval system, without permission in writing of the author.

E-mail may be sent to: Luis-Ast@VideoMathTutor.com

2

UNITS OF TIME

The basic unit of time is the Second, defined as9,192,631,770 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

3

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 =

meter

4

1 millimeter =

centimeter =

decimeter =

meter

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

5

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, justthe more typical ones.

The Yard is the basic unit of measurement of length. It isdefined as 0.9144 meters.

1 inch =

foot =

yard

1 foot = 12 inches =

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 toanother. Most values are approximate, unless otherwise noted. I willprovide one example of how to use them. This is meant more as areference. More manipulations of units are done in other Lessons.

0.393701 × centimeters = inches

2.54 × inches = centimeters <exactly>

3.28084 × meters = feet0.3048 × feet = meters <exactly>

6

1.093613 × meters = yards0.9144 × 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.

7

UNITS OF AREA

F METRIC SYSTEM F

F The Square Meter is the basic unit of measurement of area. It isdefined 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 =

square meter

8

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 isdefined 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

9

= 4840 square yards

1 square mile = 640 acres

F CONVERSIONS F

0.155 × square centimeters = square inches6.4516 × square inches = square centimeters <exactly>

10.76391 × square meters = square feet

0.092903 × square feet = square meters

1.19599 × square meters = square yards0.836127 × square yards = square meters

0.3861 × square kilometers = square miles2.590 × square miles = square kilometers

F ABBREVIATIONS F

1acre

10

UNITS OF VOLUME

F METRIC SYSTEM F

F The Cubic Meter is the basic unit of measurement of volume. It isdefined as a cube whose sides are of length one meter.

1 meter

1 meter ←1 meter→

" ← 1 cubic millimeter =

cubic centimeter

← 1 cubic centimeter =

cubic decimeter

1 cubic decimeter =

cubic meter

11

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 isdefined as a cube whose sides are of length one yard.

1 yard

1 yard ←1 yard →

← 1 cubic inch =

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→

12

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 yards0.764555 × cubic yards = cubic meters

F ABBREVIATIONS F

13

UNITS OF MASS

F METRIC SYSTEM FThe Kilogram is the basic unit of measurement of mass.It is defined as the mass of a certain cylinder made ofplatinum–iridium kept in Sèvres, France.

It is called the International Prototype Kilogram.

[

1 milligram =

gram

1 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 <Also called the short ton>

14

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 tons1.102312 × metric tons = short tons

F ABBREVIATIONS F

ounce = oz pound = lb <lower case of LB>

15

UNITS OF LIQUID CAPACITY

F METRIC SYSTEM F

The Liter is the basic unit of measurement ofcapacity (both liquid and dry). It is the volume of1 kilogram of water under specific scientificconditions.

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 isequal to 231 cubic inches.

1 drop =

teaspoon =

fluid ounce

1 teaspoon =

tablespoon = 60 drops =

fluid ounce

1 tablespoon = 3 teaspoons =

fluid ounce =

cup

16

1 fluid ounce =

pint =

quart =

gallon

1 cup =

pint = 8 fluid ounces

1 pint =

quart = 16 fluid ounces

1 quart =

gallon = 2 pints = 4 cups = 32 fluid ounces

1 gallon = 4 quarts = 128 fluid ounces

F CONVERSIONS F

0.264172 × liters = gallons3.785411784 × gallons = liters <exactly>

1.056688 × liters = quarts

0.946353 × quarts = liters

F ABBREVIATIONS F

17

UNITS OF DRY CAPACITY

F METRIC SYSTEM FSame as liquid.

F U.S. CUSTOMARY SYSTEM F

F The Bushel is the basic unit of measurement of dry capacity. It is equalto 2150.42 cubic inches.

= Although the same names are used, liquid pints and quarts areNOT the same size as dry pints and quarts.

1 pint =

quart

1 quart = 2 pints =

peck

1 peck = 8 quarts =

bushel

1 bushel = 4 pecks

F CONVERSIONS F

1.816166 × liters = dry pints

0.550610 × dry pints = liters

0.908083 × liters = dry quarts1.101221 × dry quarts = liters

0.113510 × liters = pecks

8.809768 × pecks = liters

0.028378 × liters = bushels35.23907016688 × bushels = liters <exactly>

18

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°

19

← 1 right angle = 90° =

of a circle

← 1 straight angle = 180° =

of a circle

A protractor is typically used to measure angles:

20

F UNITS OF TEMPERATURE F

F The Degree is used as the basic unit of temperature; however, there areseveral temperature scales commonly used. Two will be discussed here:Fahrenheit and Celsius.

Degrees Fahrenheit: Math Symbol: F<Read: “degrees Fahrenheit”>

212°F→

180 degrees

32°F→

← Boiling point of water

← Freezing point of water

Degrees Celsius: Math Symbol: C<Read: “degrees Celsius”>

100°C→

100 degrees

0°C→

← Boiling point of water

← Freezing point of water

21

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