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____ Sci – Density Terms and Formulas - NOTES
Date _______________________________________
DENSITY – is the amount of MASS packed into a given amount of VOLUME
1. The greater the DENSITY of an object, means more MASS is packed into the same amount of
VOLUME making the object heavier than an object with less MASS packed into exactly the same
amount of VOLUME.
2. FORMULA:
a. To calculate the DENSITY of an object you need to know or find its MASS and its VOLUME
b. DENSITY equals mass DIVIDED by volume
1. Formula: Density = _mass_
volume
(OR)
D = _m_
v
c. The LABEL for DENSITY is the combination of a metric unit of measurement for MASS “per”
a metric unit of measurement for VOLUME
1. (i.e.) g/cm3
(OR)
g/mL
2. The basic SI unit of measurement for DENSITY is “kg/m3” because the basic SI unit of
measurement for mass is the “kg” and the basic SI unit for volume is “m3”
d. (i.e.) of a DENSITY problem: mass = 27 g
volume = 9 cm3
D = _m_
v
DENSITY problem: volume = 25 mL
mass = 275g
D = _m_
v
D = _27 g_
9 cm3
D = _275 g_
25 mL
D = 3 g/cm3
D = 11 g/mL
3. To find MASS if it is not directly given:
a. Start with a “centered” BALANCE, the instrument used to measure MASS
b. Adjust “RIDERS/poises” on the BALANCE until the balance is “CENTERED” again
c. ADD the amount of the riders/POISES together if they have the SAME unit of measurement
1. (i.e.) density = g1 + g2 + g3
volume
d. (i.e.) of a density problem finding MASS and DENSITY: Substance “F” data: volume = 5 cm3;
D = _m_
mass = 4.3 g, 20 g, and 100 g
v
D = _4.3 g + 20 g + 100 g _
5 cm3
D = _24.3 g_+ 100 g _
5 cm3
D = _124.3 g _
5 cm3
D = 24.86 g/cm3
4. To find VOLUME if it is not directly given:
a. For solid VOLUME use the formula: V = l . w . h
(OR) V = l3 (square cube/block only)
b. For liquid VOLUME use a graduated cylinder and measure in “mL”
c. (i.e.) of a density problems finding VOLUME and DENSITY:
Substance “D” data: square cube w/ mass = 72 g ; 2 cm for each side
D = _m_
V
D = _72 g_
l3
D = _72 g_
23 cm
D = _72 g_
8 cm3
D = 9 g/cm3
Substance “R” data: rectangular prism w/ mass = 144 g ; length = 4 cm; width = 1 cm; height = 3 cm
D = _m_
V
D = _144 g_
l (w) h
D = _144 g_
4 cm (1 cm) 3cm
D = _144 g_
4 cm2 (3cm)
D = _144 g_
12 cm3
D = 12 g/cm3
Substance “W” data: liquid w/ mass = 544 g ; graduated cylinder = 32 mL
D = _m_
v
D = 544 g_
32 mL
D = 17 g/mL
DENSITY CONVERSION:
1. To convert MASS, use the 7 boxes for MASS to find the direction and number of movements, and make
a “NORMAL” movement.
a. (i.e.) D = _m_
v
D = _270 cg_
9 cm3
D = _2.7 g_
9 cm3
D = _0.3_ g/cm3
2. To convert SOLID VOLUME in one metric unit to another metric unit, use the 7 boxes for LENGTH
to find the direction and number of movements, then TRIPLE the movement (x 3).
a. (i.e.)
D = _m_
v
D = ____30 g _ _
.000005 m3
D = _30 g_
_5_ cm3
D = _6_ g/cm3
3. To convert LIQUID VOLUME in one metric unit to another metric unit, use the 7 boxes for LIQUID
VOLUME to find the direction and number of movements, and make a “NORMAL” movement.
a. (i.e.) D = _m_
v
D = _124 g _
.004 dL
D = _124 g_
_.4_ mL
D = _310_ g/mL
4. To convert from SOLID VOLUME to LIQUID VOLUME:
1st - Use the rules to convert from any SOLID VOLUME to “cm3”
2nd - Use the “LINK”  cm3 = mL (with a 1:1 ratio)  to get to LIQUID VOLUME
3rd - Use the rules to convert from “mL” to any other LIQUID VOLUME metric unit
a. (i.e.)
D = _m_
v
D = ____30 g _ _
.000005 m3
D = _30 g_
_5_ cm3
D = _30 g_
_5_ mL
D = _30 g_
_0.05_ dL
D = _600_ g/dL
5. To convert from LIQUID VOLUME to SOLID VOLUME:
1st - Use the rules to convert from any LIQUID VOLUME to “mL”
2nd - Use the “LINK”  mL = cm3 (with a 1:1 ratio)  to get to SOLID VOLUME
3rd - Use the rules to convert from “cm3” to any other SOLID VOLUME
a. (i.e.)
D = _m_
v
D = _124 g _
.004 L
D = _124 g_
_4_ mL
D = _124 g_
_4_ cm3
D = _124 g _ _
4,000 mm3
D = _0.031_ g/ mm3
6. To convert MASS and also convert from SOLID VOLUME to LIQUID VOLUME:
1st - Convert the MASS from its original unit of measurement to its new unit of measurement
2nd - Use the rules to convert from any SOLID VOLUME to “cm3”
3rd - Use the “LINK”  cm3 = mL (with a 1:1 ratio)  to get to LIQUID VOLUME
4th - Use the rules to convert from “mL” to any other LIQUID VOLUME metric unit
a. (i.e.)
D = _m_
v
D = ____30 g _ _
.000005 m3
D = _30000 mg_
_5_ cm3
D = _30000 mg_
_5_ mL
D = _30000 mg_
_0.05_ dL
D = _600,000_ mg/dL
7. To convert MASS and also convert from LIQUID VOLUME to SOLID VOLUME:
1st - Convert the MASS from its original unit of measurement to its new unit of measurement
2nd - Use the rules to convert from any LIQUID VOLUME to “mL”
3rd - Use the “LINK”  mL = cm3 (with a 1:1 ratio)  to get to SOLID VOLUME
4th - Use the rules to convert from “cm3” to any other SOLID VOLUME
a. (i.e.)
D = _m_
v
D = _124 g _
.004 L
D = _12.4 dag_
_4_ mL
D = _12.4 dag_
_4_ cm3
D = _12.4 dag _ _
4,000 mm3
D = 0.0031_ dag/ mm3
STEPS to Finding DENSITY Using an ALGEBRA FORMAT:
1. Write the density FORMULA, then follow it.
2. Below the FORMULA, replace any variables (LETTERS) in the formula with the NUMBERS and
UNITS of measurements they represent.
3. Follow the math ORDER of OPERATIONS rules:
a. Solve operations contained in “(PARENTHESES)” regardless of where it appears in the problem
b. Solve operations containing an “EXPONENT” regardless of where it appears in the problem
c. Work all operations from LEFT to RIGHT
1. MULTIPLY and/or DIVIDE BEFORE any addition and/or subtraction operations
2. ADD and/or SUBTRACT
4. If you need to find solid VOLUME, apply the math PROPERTIES OF MULTIPLICATION:
a. COMMUTATIVE Property of Multiplication  the ORDER of the factors makes no
difference as long as you are just multiplying
b. ASSOCIATIVE Property of Multiplication  the GROUPING of the factors makes no
difference as long as you are just multiplying
c. IDENTITY Property of Multiplication  any number or variable times ONE will give you that
same number or variable
d. ZERO Property of Multiplication  any number or variable times ZERO will give you ZERO
5. Symbols that represent the basic operation of MULTIPLICATION:
1. “x”
(e.g.) 6 x 4
a. NEVER use the “x” symbol for MULTIPLYING with an ALGEBRA format
2. “( )” (e.g.) 6 (4)
3. “ . ” (e.g.) 6 . 4
6. Symbols that represent the basic operation of DIVISION:
1. the division bracket “
”
(e.g.) 6 24
2. “ ” (e.g.) 24 6
3. the horizontal bar “ ______ ” (e.g.) 24
6
7. Solve only what each ALGEBRA step will allow, replacing that ALGEBRA operation in the next line
with the new quotient found.
a. Each ALGEBRA line above should explain the ALGEBRA line below it
b. Do NOT skip any ALGEBRA steps
8. Use the “V” ALGEBRA format to solve each ALGEBRA line, rather than a single, horizontal format
9. Remember what you do on one side of an ALGEBRA equation, you MUST DO IDENTICALLY on the
other side of the equal sign of that ALGEBRA equation.
D = m_
3
Density = 25 g/cm
v
Volume = 50 cm3
50 cm3 . 25 g/cm3 = m_
. 50 cm3
3
Mass = unknown
50 cm
1
1,250 g =
m_
1
1,250 g =
m