1. Lesson 1.06 Honors
Unit Conversion

2. Cubic unit
Cubed – is a math term that means the number or the unit is multiplied by itself three times.
cm^3 = cm x cm x cm
One cubic centimeter is equal to one milliliter, so that gives us another equivalence to use when doing unit conversions.
1 cm^3/ 1 mL same as 1mL/ 1 cm^3

4. Converting Cubic Volumes
Length Volume
m (meter) m3 (cubic meter) cm (centimeter) cm3 (cubic centimeter) mm (millimeter) mm3 (cubic millimeter)
Steps in converting cubic volumes:
Example: Convert 6.0 m^3 to cm^3
1)What are you looking for?
What unit do you want to have for your answer? This is usually given in the

5. problem or question being asked. 6 m^3 and unit cm^3
Steps
problem or question being asked.
6 m^3 and unit cm^3
2) 2) What do you already know? 
What equalities or conversions do you already know that might help you solve the
problem? Don’t forget that you know the metric prefixes and their relationship to each base unit.

6. 3) Where does the information go?
Steps
Each step in the setup is its own conversion. The numerator must be equal to the denominator.
1m = 100 cm
(100 cm/ 1 m)^3 ;use the relationship we already know and cube the entire thing
3) Where does the information go? 
Start with the given amount and its unit
and use equalities until all the units cancel

7. except the unit you need for your final answer.
Steps
except the unit you need for your final answer.
Every equivalent can be flipped((100 cm/ 1 m)^3 or (1 m/100cm)^3)—be sure to keep each number with its correct unit, but you can switch which one is in the numerator and which one is in the denominator.
- 6.0 m^3 x (100 cm/ 1 m)^3
6.0 m^3 x 100^3 cm ^3 / 1 m ^3
*100^3 = 100 x 100 x 100 =

8. You multiply everything that is on top (numerators).
Steps
4) Solve it!
You multiply everything that is on top (numerators).
Then divide by everything that is on the bottom (denominators) to get the number that goes in your answer.
Numerator = 6.0 x =
Denominator = 1
= / 1 = cm^3

9. Step 2 – 1 mL = 1 cm^3 ; 1 cm = 10^-2 m ; 10^-3 m = 1 mm
Sample Problem
Convert 40 mL to mm^3
Step 1 – 40 mL and unit mm^3
Step 2 – 1 mL = 1 cm^3 ; 1 cm = 10^-2 m ; 10^-3 m = 1 mm
Step mL x 1 cm^3/1 mL x (10^-2 m/ 1 cm)^3 x (1 mm/ 10^-3 m)^3
- 40 mL x 1 cm^3/ 1 mL x 10^-6 m^3/ 1 cm^3 x 1 mm^3/10^-9 m^3
Step 4 – 40 x 1 x 10^-6 x 1 / 1 / 10^-9
= mm^3

10. Sample Problem
B) Convert 1.8 g/cm^3 to g/mm3 Step 1 – 1.8 g/cm^3 and unit g/mm^3 Step 2 – 1cm = 10^-2 m ; 10^-3 m = 1 mm Step 3 – 1.8 g/cm^3 x (1 cm/ 10^-2 m)^3 x (10^-3 m/ 1 mm)^3 1.8 g/cm^3 x 1 cm^3/10^-6 m^3 x 10^-9 m^3/ 1 mm^3 Step 4 – 1.8 x 1 x 10^-9 / 10^-6 / 1 = mm^3