Metric Problems?

1,000 ft<------>1 inch
900 ft<------> (900/1000) x 1 inch = 0.9 inch

1cm<----> 5 km
0.1 cm<-->(0.1/1) x 5 km = (1/10) x 5 km = 0.5 km

do ratios;

1inch/1000feet = Xinch/900feet
cross multiply
900/1000 = .9 inches

1cm/5km = 0.1cm/Xkm
X = 0.1 * 5 = 0.5

900 feet x 1 inch = .9 inch
----------
1000 feet


.1cm x 5 km = .5 km
-------
1 cm

1 inch = 1 x 1000 feet
1 feet = 1 x 1/1000 inch

900 feet = 900 x 1/1000 inch = 9/10 inch
--------------------------------------------------------
1 cm = 1 x 5 km
1 km = 1 x 1/5 cm

0.1 cm = 0.1 x 5 km = 0.5 km

I'll preface my answer with : "This question is simply rediculous."

Now that that's over with, you just start with what you're given, and multiply by the converstion factors making sure the labels cancel:

900 ft * (1/1000 in/ft) = .9 in

Here, the "ft" cancel out, leaving only "in" as the remaining label.

.1cm * (5 km/cm) = 0.5 km

The "cm" labels cancel out, leaving only "km" as the remaining label.

0.9 Inch
1 Inch=1000 Ft
so
1/1000= 1Ft
1ft =1/1000 Inch
900 Ft
900ft *1 ft =900* 1/100
.
.
900 Ft=0.9Inch

I don't quite understand your question but here goes, let's turn inches into x and feet into y.

1X=1000Y
900Y=0.9X
as in 0.9 inches

and second question: cm=X and km=Y

1X=5Y
0.1X=0.5Y
as in 0.5km

hope this was what you were asking for.

1 inch / 1000 feet = ? / 900 feet
? = 900/1000
? = 0.9 feet

5 km / 1 cm = ? / 0.1 cm
? = 0.1(5)
? = 0.5 km

0.9 inches represent 900 feet on this scale.
Since 900 is 90% of 1000, take 90% of one inch.

if 1 cm = 5 km, then 0.1 cm = 0.5 km just shift the decimal.