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