Conversion of Scale

1. Conversion of Scale

Converting a statement measure into a Representative fraction (R.F.) -
When given the objective scale and turning it into a demonstrator, we need to take the following two step .
steps.1
The distance of the map is given in the unit i.e. if the surface if the distance is in the metric system (km, meters) then its centimeters draw and if it is in the British system (miles, yards) then its make an inch.  Step 2.
Use this formula

                                                             Distance on the map
Representative  Fraction (R.F.) =  ----------------------------------------
                                                             Distance on the ground

Example 1. The plot of a map is 5 cm: 1 km.  Find its Representative fraction (R.F.).
Step 1. Change the distance of the surface to cm, because the distance on the map is in cm.  1 km = 1,00,000 cm.
Step 2.
                 Distance in centimeters on the map
RF=         ----------------------------------------------------------
                Distance in centimeters on the ground
   
                      5                         1
RF=     ---------------------- =   --------------------
                      1,00,000             20,000
                                            
                                                 (The fraction is always 1.)
RF= 1: 20,000


Example 2. 1 inch: 8-mile statement scale

Convert to Representative fraction (R.F.).
  Step 1. Change the distance of the ground in inches.
             Because the distance of the map is in inches.

           8 mile = ৪ x 63,360 = 5,06,880 inches
          (1 mile 63,360 in)
Step 2.
              Distance on the map in inches
R.F.  = ----------------------------------------------------
            Distance on the ground in inches
                   1
RF= -------------------------
          5,06,880                 (The numerator is always 1.)
R.F.  =1: 5,06,880

R.F.  = 1: 5,06,880 Answer

Converting the R.F.  into Statement of Scale

We can use any system of measurement when making a predictive measure from a different display.  Nevertheless we are asked to convert to a particular measurement system.  For this also, we have to take two steps.
Step 1. Same unit with both numerator and denominator.
  Step 2. According to the measurement system described in the distance of the ground to change in km or miles.

Example 3. On a map RF      1
                                             --------------------
                                               3,00,000
has given.  Make a descriptive measure to show it in km.

Step 1. R.F.  ;  Read it metric system
Read in
1cm: 3,00,000cm
steps 2. Change the distance of the surface to km.
                               1
        1 cm =   --------------------   km
                         1,00,000


                              3,00,000
3,00,000 cm =  ------------------ =3 km
                              1,00,000

Ans. Statement Measure 1 cm: 3 km



Example 4. If the Representative fraction 1: 10,00,000 then convert it to a test scale to show miles.
Step 1. Read  R.F.       1              in British system
                                --------------------
                                 10,00,000
1 inch: 10,00,000 inch

Step 2. Convert the distance of the surface into miles.
                       1
1 inch:     ----------------- mile
                     63,360

                                          10,00,000
     10,00,000   inch:    = -------------------  
                                               63,360
= 15.78 mile

Ans. Statement measuring scale 1 inch: 15.78 mi.