Question

A map of Levi’s property is being made with a scale of 2 centimeters : 3 meters. What is the scale factor?

Answer 1

Answer: The scale factor is: " 2 : 300 " .
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Step-by-step explanation:
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2 cm : 3 m ;
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Convert: "2 cm " to the value in "m" .

Note the exact conversion: "100 cm = 1 m" .
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2 cm * (1 m / 100 cm) = (2/100) m = 0.02 m .

So we rewrite: "2 cm: 3 m " ; as:
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0.02 m : 3 m ;

The units of "m" cancel out ; since "m/m = 1" ;
and we are left with:

0.02 : 3 ; or, write as: 0.02/3 ;

Now, multiply BOTH the numerator and the denominate by "100" ; to get rid of the decimal; since "scale factors" in maps do not use "decimals" ;

"0.02 / 3 " = [ (0.02)*100 ] / [(3 * 100)] = 2/300 ;
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Answer: The scale factor is: " 2 : 300 " .
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Answer 2

1:150

Step-by-step explanation:

Hello

the scale factor is the ratio that exists between the measurements of a map with the originals ,the scale is the relationship between the real dimensions and those of the drawing that represents reality on a plane or a map.the scale factor is dimensionless

for a map a scale of reduction is used

`sf=(length\ on\ reality \ )/(length\ on\ map \ )`

Step 1

the scale factor of 2 centimeters : 3 meters means that, if we measure 2 cm in the map , it is 3 meters on the reality

Let

Length on the reality=3 m

Length on the =2 cm

replacing

`sf=(length\ on\ reality \ )/(length\ on\ map \ )\\sf=(3\ m)/(2\ cm)`

to cancel units is need convert cm into m, or m

1 m =100 cm

3m = x? cm

x=3*100 cm

x=300 cm

Step 2

replacing

`{length\ on\ map \ }\\sf=(300\ cm)/(2\ cm)\\sf=150`

the scale factor is 150, usually is written 1:150, that means that any length in the plane must be multiplied by 150 to know the length in reality

Have a great day