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Map Scale
MAP SCALE…
• A SCALE shows the relationship between the distance on a map and the ACTUAL distance on the EARTH’s SURFACE
• Scale can be represented in 3 ways: 1) direct statement/verbal 2) Line scale 3) Representative Fraction Scale (RF)
DIRECT STATEMENT…
• Uses words to describe the relationship between a distance on a map and a specific distance on the Earth’s surface
FOR EXAMPLE: 1 cm to 10 km OR 1 cm = 10 km
What does this direct statement mean?
For example…
• If you have measured the distance between Hamilton and Toronto and found it to be 25 cm on the map, and the direct statement reads 1 cm = 2 km, how far would it be in km?
HOW DO WE FIGURE THIS OUT?
Solution…
1 cm = 2 km25 cm X
1 x X = 2 x 25
X = 50
Therefore, the actual distance between Hamilton and Toronto is 50 km
5 STEP PROCESS
1) Write down the statement:1 cm = 2 km
2) Add in the information you know: 1 cm = 2 km25 cm X
3) Eliminate (the same) units: 1 cm = 2 km25 cm X
4) Cross Multiply:1 x X = 25 x 2
5) Therefore statement…
LINE (Linear) SCALE…
• A special kind of ruler on the map that is divided into equal units of distance
• Always includes the units of measurement on the Earth’s surface
SO, HOW DOES THIS WORK?
REPRESENTATIVE FRACTION SCALE (R.F)…
• The scale is written as a ratio FOR EXAMPLE: 1:50 000
• This means: ONE unit on the map represents 50 000 of the same units on the Earth’s surface
1:50 000
The SECOND term of the ratio:– Represents the
distance on the Earth
– Same unit of measurement as the first term
The FIRST term of the ratio:– is always 1– Represents the
distance on the map in units
SCALE CONVERSION
1 km = 1 000 m1 m = 100 cm
1 km = 100 000 cm
CONVERTING RF TO DIRECT STATEMENTS
From RF scale direct scale: divide the right side of the equation by 100 000, to change centimetres to kilometres
convert 1:50 000 RF to direct statement
1:50 0001 cm = 50 000 cm1 cm = 50 000 km
100 0001 cm = 0.5 km
or1 cm = 500 m
CONVERTING DIRECT STATEMENTS TO RF From direct statement scale RF scale:
multiply the right side of the equation by 100 000 to change kilometres into centimetres
convert 1 cm = 2.5 km into a RF
1 cm = 2.5 km1 cm = (2.5 x 100 000) cm
1 cm = 250 000 cmor
1:250 000
IN SUMMARY… Converting R.F to Direct Statements:
divide right side by 100 000 to change cm km
Converting Direct Statements to R.F: Multiply right side by 100 000 to change km cm
QUESTION:
What does 1 cm = 0.5 km mean?
Answer: 1cm on the map represents 0.5 km on the earth’s surface
QUESTION:
Direct Statement: 1 cm = 35 kmIf the map distance between
points A and B is 9 cm, what is the real distance?
Answer: 9cm = 315km
QUESTION:
Direct Statement: 1 cm to 250 kmIf two places are 17 cm apart on
the map, what is the actual distance between them?
Answer: 17cm = 4250km
QUESTION:
In your own words, what does 1:250 000 mean?
Answer: One centimeter on ant map represents 250 000 cm on the earth’s surface
What does 1:3 000 000 mean?
QUESTION:
Convert the RF into a DIRECT STATEMENT
1:250 000
Answer: 1cm = 2.5km OR 1cm to 2.5km
QUESTION:
Convert the RF into a DIRECT STATEMENT
1:63 000 000
Answer: 1cm = 630km or 1cm TO 630km
QUESTION:
Convert the direct statements to RF scales
1 cm to 5 km
Answer: 1cm = 500 000cm
QUESTION:
Convert the direct statements to RF scales
1 cm to 25 km
Answer: 1:2 500 000
QUESTION:
The line scale on a map indicates that 4 cm represents 20 km.
What is the RF?
Answer: 1:500 000
QUESTION:
The line scale on a map indicates that 1.5 cm represents 50 km.
What is the RF?
Answer: 1:3 333 333