Exercise 11 Page 315

We want to complete the given conversion using a dimensional analysis. 200cL = L First, let's identify the conversion rate between centiliters (cL) and liters (L). 100cL=1LThis means that the conversion factor between centiliters and liters can be expressed by the following fraction. 1L/100cL Now, we want to convert 200 centiliters to liters using dimensional analysis. To do this, we can multiply the factor by 200cL. Let's do this! 200cL * 1L/100cL &= /L = L Let's now perform the multiplication and divide out common units.

200cL * 1 L/100cL

CrossCommonFac

Cross out common factors

200cL * 1 L/100cL

SimpQuot

Simplify quotient

200 * 1 L/100

MoveLeftFacToNum

a*b/c= a* b/c

200 * 1 L/100

IdPropMult

Identity Property of Multiplication

200L/100

MovePartNumRight

a* b/c=a/c* b

200/100L

Our multiplication simplifies to 200 100 liters. 200cL * 1L/100cL &= 200/100L = L Finally, the quotient of 200 and 100 is 2. 200cL * 1L/100cL &= 200/100L = 2L We found that 200 centiliters are equal to 2 liters. 200cL=2L