Measurement Units, Calculations, and Scales

 

	This Project has been funded with support from the European Commission.  This communication reflects the views only of the author, and the Commission can not be held responsible for any use which may be made of the information contained therein.

 

Objectives

Upon completion of this unit you shall be able to:

• Describe the main scales of measurement and the relationships between different scales         
• Solve related problems

 

Introduction

Lengths

We talked about length, area and volume, but so far we haven’t discussed any measurement units yet. The first measurement unit that will be discussed here for length is the meter. All lengths are measured in meters and its divisors or multiples. Other units of length and their equivalents in meters are as follows:

1 millimeter = 0.001 meter
1 centimeter = 0.01 meter
1 decimeter = 0.1 meter
1 kilometer = 1000 meters
We symbolize these lengths as follows:
1 millimeter = 1 mm
1 centimeter = 1 cm
1 meter = 1 m
1 decimeter = 1 dm
1 kilometer = 1 km

We also have:

1 m = 1000 mm
1 m = 100 cm
1 m = 10 dm
1 km = 1000 m

Let’s transform some values from one unit to another: how many centimeters is 13,24 meters?

In decimeters we have

In millimeters

And in kilometers

since .

Surfaces

Surfaces are measured in squares of length units, that is square meters. To put it simply, a square meter is the surface of a square having the sides of 1 meter each.
Besides square meters, denoted by , we will have the following additional units:

1 square centimeter = 1.
1 square meter = 1
1 are = 1 100
1 hectare = 1  = 10000  
1 square kilometer = 1 =1000000

An are is the area of a square having all sides equal to 10 m, and a hectare is the area of a square having all sides equal, each 100 meters long.

We also have

Let’s convert from square km to other units the following:

 

Volumes

The standard unit of volume in the metric system is the liter. One liter is equal to 1000 cubic centimeters in volume, or the volume of a cube having all sides equal to 10 cm. Therefore

1 l = 1000 = 1 = 1000 cc

Other units of volume and their equivalents in liters are as follows:

1 milliliter = 0.001 liter
1 centiliter = 0.01 liter
1 deciliter = 0.1 liter
1 hectoliter = 100 liters
1 kiloliter = 1000 liters

Alternate measurement units are cubic meters, cubic centimeters, and the conversions are as follows:

1 cubic meter = 1 =1000 l= 1 kl
1 cubic decimeter = 1  = 1 l
1 cubic centimeter= 1  = 0,001 l = 1 ml

From these units, we see that 1000 milliliters equal 1 liter; so 1 milliliter equals 1 cubic centimeter in volume. We symbolize these volumes as follows:

1 milliliter = 1 ml
1 centiliter = 1 cl
1 deciliter = 1 dl
1 liter = 1 l
1 hectoliter =1 hl
1 kiloliter = 1 kl

Let’s calculate the volume of a cube having the sides of 1,5 meters:

Mass

The standard unit of mass in the metric system is the gram. Other units of mass and their equivalents in grams are as follows:

1 milligram = 0.001 gram
1 centigram = 0.01 gram
1 decigram = 0.1 gram
1 kilogram = 1000 grams

We symbolize these masses as follows:

1 milligram = 1 mg
1 centigram = 1 cg
1 decigram = 1 dg
1 gram = 1 g
1 kilogram = 1 kg

For reference, 1 gram is about the mass of a paper clip. One kilogram is about the mass of a liter of water.

Let’s transform 155 grams in other units:

Time

The basic unit for measuring time is the second, denoted by the letter . Other units are minutes, hours, days, weeks, and years.
The following conversions are useful when working with time:

1 minute = 60 seconds
1 hour = 60 minutes = 3600 seconds
1 day = 24 hours
1 week = 7 days
1 year = 365 1/4 days (for the Earth to travel once around the sun)

In practice, every three calendar years will have 365 days, and every fourth year is a "leap year", which has 366 days, to make up for the extra quarter day over four years. The years 1992, 1996, 2000, and 2004 are all leap years. This gives us a total of 52 complete 7 day weeks in each calendar year, with 1 day left over (or 2 in a leap year).

The year is divided into 12 months, each of which has 30 or 31 days, except for February, which has 28 days (or 29 days in a leap year).

Let’s calculate how many seconds are there in 3 hours:

and how many hours in 2 weeks and 3 days:

therefore 2 weeks and three days will have  and thus

Temperature

Temperature is expressed in degrees Celsius in the metric system. The boiling point of water (at sea level) is 100°Celsius, or 100°C. The freezing point of water (at sea level) is 0° Celsius. A hot day is about 30° Celsius.

Decimals in measurement

We use decimals to specify units of measurement when we need more precision about length, volume, mass, or time. For example, when specifying the height of a person 1.63 meters tall, to say that person is 1 or 2 meters tall doesn't give us a very good idea of how tall that person really is.
The prefixes for the different units of length, volume, and mass in the metric system obey the following rules:

So for example:

1 hectometer = 100 meters
1 centigram = 0.01 gram
3 milliliters = 3 × (0.001 liters) = 0.003 liters
0.9 kilometers = 0.9 × (1000 meters) = 900 meters