Transcript Lesson 1.06 Honors Unit Conversion Cubic unit • Cubed – is a math term that means the number or the unit is multiplied by.

Lesson 1.06
Honors
Unit Conversion
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
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
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.
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
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 = 1000000
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 1000000 = 6000000
- Denominator = 1
= 6000000 / 1 = 6000000 cm^3
Sample Problem
A) 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 3 - 40 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
= 40000 mm^3
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
= 0.0018 mm^3