Exercise 12 Page 315

We want to complete the given conversion using a dimensional analysis. 2.5kg = g First, let's identify the conversion rate between kilograms (kg) and grams g). 1kg=1000gThis means that the conversion factor between kilograms and grams can be expressed by the following fraction. 1000g/1kg Now, we want to convert 2.5 kilograms to grams using dimensional analysis. To do this, we can multiply the factor by 2.5kg. Let's do this! 2.5kg * 1000g/1kg &= /g = g Let's now perform the multiplication and divide out common units.

2.5kg * 1000 g/1kg

CrossCommonFac

Cross out common factors

2.5kg * 1000 g/1kg

SimpQuot

Simplify quotient

2.5 * 1000 g/1

MoveLeftFacToNum

a*b/c= a* b/c

2.5 * 1000 g/1

Multiply

Multiply

2500g/1

MovePartNumRight

a* b/c=a/c* b

2500/1g

Our multiplication simplifies to 2500 1 grams. 2.5kg * 1000g/1kg &= 2500/1g = g Finally, the quotient of 2500 and 1 is 2500. 2.5Kg * 1000g/1Kg &= 2500/1g = 2500g We found that 2.5 kilograms are equal to 2500 grams. 2.5kg=2500g