I'm Stuck. Please Help. (Dimensional Analysis)

Question

1. Convert each of the following:

A. 376 mL to L:

B. 5.910 g to kg:

C. 1290000000 mm to km:

D. 1.2 x 1024 cm to m:

E. 9.22 x 10(-19) kL to mL:

F. 10.0 kg to mg:

1. Use the equation d=r*t for the following:

A. You run at the average speed of 4.05 m/s for 225 seconds. What is the distance, in meters, traveled?

i. What is the distance in kilometers?

B. Your car travels at an average speed of 50.0 km/hr. How far, in kilometers, does it go in 2.8 hours?

i. What is the distance in cm?

C. A plane travels at an average speed of 812 km/hr. How far does it travel, in kilometers, in 90 minutes?

1. What is the distance in meters?

Answer 1

I'm not going to all of them, but will demonstrate how to use dimensional analysis to solve these.

You set up dimensional analysis so that you cancel the units you don't want and leave the units you do want. Of course, to do this, you MUST know the conversion factors to use.

A. 376 mL to L: 376 ml x 1 L / 1000 ml = 0.376 L (you cancel ml leaving you with L)

B. 5.910 g to kg: 5.910 g x 1 kg / 1000 g = 5.910x10^-3 kg (cancel g leaving you with kg)

C. 1290000000 mm to km: 1.29x10⁹ mm x 1 km / 1x10⁶ mm = 1.29x10³ km (cancel mm leaving km)

distance = rate x time (d = r x t)

A. You run at the average speed of 4.05 m/s for 225 seconds. What is the distance, in meters, traveled?

i. What is the distance in kilometers?

4.05 m/s x 225 s = 911.25 m (cancel s leaving m) answer to the first part

911.25 m x 1 km / 1000 m = 0.91125 km (cancel m leaving km) answer to the 2nd part

Try to do the others by yourself. They aren't that difficult. If you have to look up the conversion factors, then do so.