Chapter 10
Measurement
Section 10.1
Systems of Measurement
Measuring an object is to assign a number to a feature of it in some sort of
standardized way. The way the number is assigned usually has several common
properties.
1. The measurement number is never negative.
2. The measurement number being zero indicates none of what you are
measuring is present.
3. The more of the feature you are measuring there is the larger the
measurement number you assign.
4. A standard unit is used so that the measurement can be replicated.
For example if you go to buy a pair of pants there are two features of the pants
that a number has been assign to; the waist and the inseam. This is a positive
number that matches the distance around your waist. A waist size of 32 is smaller
than a waist size of 38.
Features of Geometric Shapes and Physical Objects
The features of geometrical shapes we will be interested in measuring are length,
area and volume (capacity). The features of physical objects we will be interested
in measuring are mass (weight) and temperature.
Measuring Length
To measure the length of a line segment you want to find how many unit
segments laid end to end will be congruent to the segment you want to measure.
The number of units that are used is the measure in that length of unit. Look at
the example below of using red, green and orange units to measure the black
segment.
1 Black Segment =
2 Red Segments =
4 Green Segments =
8 Orange Segments =
Measurement Systems: English vs Metric
The English system of measure based its lengths on certain objects or body
parts. The common units that are used are: inch, foot, yard and mile. The metric
system of measure based its lengths on the speed of light. The common units for
it are: millimeter, centimeter, meter, kilometer.
The units that are chosen by a child to measure (or approximate) a distance come
from setting up benchmarks which are common measurements of things in the
environment.
For Example:
The length of a standard size sheet of paper is about 1 foot. (The paper is a
benchmark for 1 foot.)
A football field is 100 yards long. (The football field is a benchmark for 100 yards.)
A meter is about the length of my leg. (My leg is the benchmark for a meter.)
A mile is about 17 football fields in length. (17 football fields are a benchmark for a
mile.)
Units for the English and Metric Systems
English System
1 foot = 12 inches
1 yard = 3 feet
1 mile = 5280 feet
Metric System – These prefixes and symbols are
used with the metric system units: meters (m),
grams (g) and liters (L).
Prefix
kilo
hecto
decka
deci
centi
milli
Symbol
k
h
dk
d
c
m
Number
1000
100
10
1
1
10
1
100
1
1000
Other Measurements
Sometimes we wish to measure other qualities of an object (or person) besides
length. Some of the other things that are measured include:
•Mass (weight) – units include: pounds, ounces, grams, kilograms
•Capacity (volume) – units include: ounces, cups, quarts, gallons, milliliters, liters
• Time – units include: seconds, minutes, hours, days, weeks, years, decades
• Temperature – units include: Fahrenheit, Celsius
Unit Conversion
To convert from one unit to another we use an idea called dimensional analysis
or cancellation of units. You start with the units you have and on the other side of
the equation you put the units you want to change to. You write down fraction or
fractions with the correct units so they cancel and leave you with what is on the
other side. For example if we wish to change 250 yards into miles.
250 yard

3 feet
1 yard
yards cancel

1 mile
5280 feet
feet cancel
= (250)(3)
5280
mile = .142045 mile
Convert 40 hours into weeks.
40 hour


1 day
24 hour
cancel hours
1 week
7 day
=
40
week
= .238095 week
(24)(7)
cancel days
Precision
The smaller a unit is the more precise it is (i.e. the more accurately you know
the value of what you are trying to measure). For example yards are more
accurate than miles. Feet are more accurate than yards. Inches are more
precise than feet.
Which of the following are more precise?
about 31 inches
or
about 2.5 feet