a Measure the appropriate distance and use it to evaluate the scale.
B
b Express the scale using only inches by converting miles to inches.
A
a 1.75in.:0.47mi
B
bScale Factor: 1:17 017
Meaning: The actual distance is approximately 17 017 times greater than the distance on the map.
Practice makes perfect
a We are given that the actual distance between the intersections of two streets with 4th Street is 0.47 miles, and we are asked to estimate the scale of the given map. Using a customary ruler, we can see that the appropriate distance on the map is 1 34 inches.
The scale of the map: 1 34in.: 0.47mi
We can simplify the scale by rewriting 1 34 as a decimal.
1 34in.:0.47mi
⇓
1.75in.:0.47mi
b In this part, we are asked to find the approximate scale factor of the map. To do this, we should express the scale only in inches. Let's evaluate how many inches we have in one mile.
1mi=1* 5280ft=1*5280*12in.=63360in.
Since there are 63360 inches in one mile, we will multiply 0.47 by 63360 to convert it to inches.
0.47mi=0.47*63360in.≈29 779
With this information, we can rewrite the scale we found in the previous part using only inches.
1.75in.:0.47mi
⇓
1.75:29 779
Finally, to determine the scale factor we will divide both sides of above scale by 1.75.
1.75:29 779
⇓
1:17 017
Therefore, the scale factor of this map is approximately 1:17 017. This means that the actual distance is approximately 17 017 times greater than the distance on the map.
