5-Scale

Report
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
25 cm
=
2 km
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 km
25 cm
X
3) Eliminate (the same) units:
1 cm = 2 km
25 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 FIRST term of
the ratio:
The SECOND term
of the ratio:
– is always 1
– Represents the
distance on the
map in units
– Represents the
distance on the
Earth
– Same unit of
measurement as
the first term
SCALE CONVERSION
1 km = 1 000 m
1 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
1:50 000
1 cm = 50 000 cm
1 cm = 50 000 km
100 000
1 cm = 0.5 km
or
1 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 km
1 cm = (2.5 x 100 000) cm
1 cm = 250 000 cm
or
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 km
If 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 km
If 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

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