Saturday, 2 January 2016

Metric Units : Linear Units : Mass Units : Density Units : Site Engineering Units :

Metric Unit



Metric Units:
In mathematics, we come across with physical quantities, such as - length, weight, temperature etc. These quantities are associated with some magnitude and a unit. Magnitude is a constant number, while the unit is a standard according to which the magnitude has been expressed. Each physical has its predefined unit of measurement. There are metric units of measurement in mathematics. Metric units are one of the most important and useful topics.

The metric system is defined as an international decimal system of measuring physical quantities. Metric units or metric measurement units are used for the purpose of calculating units of other quantities. Metric units are the most common system for measuring different types units in all over the world. It is widely utilized scientifically, commercially and personally. Metric units are the base units that are used to formulated other larger and smaller units from the standard set of prefix in powers of ten. Metric system of units is also termed as SI system. It defines the 7 basic units which are length, mass, time, temperature, luminous intensity, electric current and amount of substance. The units of all other quantities are derived from these 7 basic units.
Let us see some metric measurement units.

In Metric System, 
  • The unit of Length is meter (m) 
  • The unit of Mass is kilogram (g) 
  • The unit of Time is second (s)
What are Metric Units
Metric units is a system for measuring different type of units. This system is used for the purpose of calculating an international decimalised system of measurement. In the metric system other units of measurement are obtained by multiplying and dividing by powers of 10. The metric system has standard units of measurement mainly used in the problems related to the length, area, volume, mass, temperature, electricity and time.
Metric units system has some basic units:

                                         1. m the meter for length

                                         2. Kg the kilogram for mass

                                         3. S the second for time

                                         4. A the ampere for electric current

                                         5. K the kelvin for Temperature

                                         6. cd the candela for luminous intensity

                                          7. mol the mole for Amount of substance

 

1. Metric Units of Length

    a) The metric units of length are:

             
1 kilometer = 1000 meters

1 hectometer = 100 meters

1 decameter = 10 meters
A meter is the basic unit of length

1 decimeter = 110 meter

1 centimeter = 1100 meter

1 millimeter = 11000 meter

2. Metric Units of Mass

In the metric system the standard unit of mass is given as "gram". Some more units of mass and their equivalent units are given below:

1milligram = 0.001 gram

1centigram = 0.01 gram

1decigram = 0.1 gram

1kilogram = 1000 grams

 The symbolic form of this masses are given as follow:
1milligram = 1 mg 

1centigram = 1 cg

1decigram = 1 dg

1gram = 1 g

1kilogram = 1 kg

1 gram mass is about the mass of a paper clip.

one kilogram mass is about the mass of one liter of water. 
 3. Metric Units of Volume 
Metric units of volume are:

1 Milliliter = 0.001liter

1 Centiliter = 0.01liter

1 Deciliter = 0.1liter

1 Kiloliter = 1000liters

The symbolic form of the above measurements are given below:

1 Milliliter = 1 ml

1 centiliter = 1 cl

1 deciliter = 1 dl

1 liter = 1 l

1 kiloliter = 1 kl 

 4. Metric Units of Time 
Here are some useful conversions are given for the time.

1 minute = 60 seconds

1 hour = 60 minutes = 3600 seconds

1 day = 24 hours

1 week = 7 days

1 year = 365 14 days 

  5. Metric Units of Capacity
      
Metric units of capacity are:
1 centiliter = 10 milliliters
1 deciliter = 10 centiliters
1liter = 10 deciliters
1cubic meter = 1000 liters

6. Metric Units of Measurement


     
Metric units and measurements of length, mass, volume and temperature:
a) Linear Measure
1 meter (m) = 10 decimeters (dm) = 100 centimeter (cm)
1 centimeter (cm) = 10 millimeters (mm) = 0.01 meter
1 decimeter (dm) = 10 centimeters(cm) = 0.1 meter
1 dekameter (dam) = 10 meters
1 kilometer (km) = hectometers = 1,000 meters
1 hectometer (hm) = 10 dekameters = 100 meters

b) Mass
1 gram = 1000 milligram
1 gram = 100 centigram
10 decigrams = 1 gram (g) = 1,000 milligrams
1 kilogram = 1000 grams
10 dekagrams = 1 hectogram (hg) = 100 grams
10 hectograms = 1 kilogram (kg) = 1,000 grams
10 milligrams (mg) = 1 centigram (cg)
10 centigrams = 1 decigram (dg) = 100 milligrams

c) Volume Measure

1 kiloliter = 1000 liters
1 liter = 1000 milliliter
1 liter = 100 centiliter
1 liter = 10 deciliter
1 centiliter (cl) = 10 milliliter (ml)
10 centiliters = 1 deciliter (dl) = 100 milliliters
10 deciliters = 1 liter (l) = 1,000 milliliters

d) Temperature

Celsius Fahrenheit Kelvin
100 212 373 (Boiling point of water)
30 86 303 (a hot day)
20 68 293 (Average room temperature)
0 32 273 (Freezing point)
- 40 - 40 233 (Celsius and Fahrenheit are same)


Converting Metric Units


                
Metric units system convert larger units to smallest unit or smallest unit to larger unit
We Know that 
1 km = 1000 m
1 m = 100 cm
1 cm = 10 mm
               From here we can say that, a kilometre is a larger unit than a metre, a metre is a larger unit than a centimetre and a cm is a larger unit than millimeter.

                
Let see how to convert metric units:
(1)  To convert length from a large unit into a small unit, multiply by the relevant power of 10.
1 km = 1000 m = 103 m
1 m = 100 cm = 102 cm
1 cm = 10 mm = 101 mm

(2) To convert length from a small unit into a large unit, divide by the relevant power of 10.

1 mm = 110 cm = 10-1 cm
1 cm = 1100 m = 10-2 m
1 m = 11000 km = 10-3 km
Solved Examples
Question 1: Convert 5 km to mm
Solution:
Step 1:
              1 km = 1000 m
           5 km = 5 x 1000 m
                    = 5000 m
Step 2:
                1 m = 100 cm
      5000 m = 5000 x 100 cm
                   = 500000 cm
Step 3:
               1cm = 10 mm

 500000 cm = 500000 x 10 mm
                   = 5000000 mm

Question 2: Convert 10 m to km.
S
olution:
                1 m = 10-3 km

          10 m = 10 x 10-3 km

                   = 101000 km

                   = 1100 km

                   = 10 -2 km

Converting between Metric Units

Solved Examples
Question 1: To convert 1000 acres to Hectares.
Solution:
         Here we have to convert acres to Hectares.
1 acres = 0.404685642 hectares
Therefore,
1000 acres = 0.404685642 hectares [xx] 1000 acres
                  = 404.685642
        
The answers for 1000 acres are equal to 404.685642 Hectares.
Question 2: To convert 700 Hectares to Square feet.
Solution:
          Here we have to convert Hectares to Square feet.
1 hectare = 107 639.104 square feet
Therefore,
700 Hectares = 107 639.104 square feet [xx] 700 Hectares
                      = 75347372.8 sq.ft
The answers for 700 Hectares are equal to 75347372.8 Square feet.
 
Question 3: To convert 100 Kilometers (km) to Miles.
Solution:
     
Here we have to convert Kilometers (km) to Miles.
1 kilometer (km) = 0.621371192 miles
Therefore,
100 km = 0.621371192 miles [xx] 100 km
             = 62.1371192 miles
The answers for 100 Kilometers (km) are equal to 62.1371192 miles.
  

Question 4:To convert 300 millimeters to inches.
Solution:
       
Here we have to convert millimeters (mm) to inches
1 millimeter (mm) = 0.0393701 inches
Therefore,
300 mm = 0.0393701 inches [xx] 300 mm<
              = 11.81103 inches
The answers for 300 millimeters (mm) are equal to 11.81103 inches.
 
Question 5: To convert 600 centimeters to meters.
Solution:
           
Here we have to convert centimeters (cm) to meters.
1 centimeter (cm) = 0.01 meters
Therefore,
600 cm = 0.01 meters [xx] 600 cm
             = 6 meters
The answers for 600 centimeters (cm) are equal to 6 meters.
Metric Units Chart

Metric Units Chart for Mass

1000 grams = 1 kilogram
1000 kilograms = 1 ton

Metric Units Chart for Capacity
10 milliliters = 1 centiliter
10 centiliters = 1 deciliter
10 deciliters = 1 liter
1000 liters = 1 cubic meter

Metric Units Chart for Length

10 millimeters = 1 centimeter
10 centimeters = 1 decimeter
10 decimeters = 1 meter
10 meters = 1 decameter
10 decameters = 1 hectometer
10 hectometers = 1 kilometer

Metric Units Chart for Area

100 square mm = 1 square centimeter
10 centimeters = 1 decimeter
10000 square cm = 1 square meter
100 square m = 1 acre
100 acres = 1 hectare
100 hectares = 1 square kilometer

Abbreviations For Metric Units

Abbreviations
      For Length
                 1 centimeter = 1 cm
                 1 meter = 1 m
                 1 decimeter = 1 dm
                 1 kilometer = 1 km
Mass
                 1 milligram = 1 mg
                 1 centigram = 1 cg
                 1 decigram = 1 dg
                 1 gram = 1 g
                 1 kilogram = 1 kg
Temperature
                 degree kelvin = k
                 degree Celsius = 0c
                 Fahrenheit = F
For Volume
                  1 milliliter = 1 ml
                  1 centiliter = 1 cl
                  1 deciliter = 1 dl
                  1 liter = 1 l
                  1 kiloliter = 1 kl
Examples on Converting Metric Units

Below are the examples on converting metric units - 

 Solved Example

Question 1: Convert 4 km into lower units.
Solution:
               
4 km = 40 hm (4 × 10) = 4 × 101 hm
                     = 400 dam (4 × 100) = 4 × 102 dam
                     = 4000 m (4 × 1000) = 4 × 103 m
                     =40000 dm (4 × 10000) = 4 × 104 dm
                     = 400000 cm (4 × 100000) = 4 × 105 cm
                     = 4000000 mm (4 × 1000000) = 4 × 106 mm
Question 2: Express 1267547 mm into higher units.
Solution:
                12675477 mm = 126754.7cm[1267547/10] =1267547 x 10-1 cm
                                     =12675.47dm[1267547/100] =1267547 x 10-2 dm
                                     = 1267.547m[1267547/1000] =1267547 x 10-3 m
                                     =126.7547dam[12.6754]/10000 = 1267547 x 104 dam
                                      =12.67547hm[1267547/100000] =1267547 x 10-5 hm
                                      =1.267547km[1267547/1000000] =1267547 x 10-6 km
Question 3:Convert 7m into millimeter.
Solution:
          We know that ,
1m =1000mm
Therefore ,
7m = 7*1000mm
=7000mm


Question 4:Express 10kg5dag in grams
Solution:
          
We know that,
           1kg =1000g
           1dag =10g
Therefore,
          10kg5dag = 10 *1000g +5 *10g
                          =10000g +50g
                          =10050g
Metric Units Practice Problems


Practice problem to help with metric calculation:


Practice Problems

Question 1: Convert 6m into millimetre.

Question 2: Express 2769 g in kilograms.

Question 3: Convert 25 kl 37 l into litres.


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