Density Remediation

Density Remediation

D =

MV

First, enter the givens into the density table.

48,000 tons

1. Find the density of a substance whose mass is 48,000 tons and volume is 0.000600 pL?48,000 tons 0.000600 pL?

0.000600 pL

D =

MV

Next, enter the units from the mass and volume into the left side of the density table.

1. Find the density of a substance whose mass is 48,000 tons and volume is 0.000600 pL?

48,000 tons = ? pL = ? tons

0.000600 pL

No conversion is necessary.

D

Use the formula triangle to determine the correct formula.


V

M ÷

MV

xD =

D =

MV

Substitute the values into the equation.


48,000 tons = ? pL = ? tons

0.000600 pL

D = M/VD = (48,000 tons) / (0.000600 pL)

D =

MV

Divide and round to the LEAST number of significant digits.


48,000 tons = ? pL = ? tons

0.000600 pL

D = M/VD = (48,000 tons) / (0.000600 pL)

D = 8.0 x 107 tons/pL

D =

MV


49.7 lbs1 Tm3

2. Find the volume of a substance whose density is 49.7 lbs/Tm3 and mass is 204,900 ng?49.7 lbs/Tm3 204,900 ng ?

204,900 ng

D =

MV

Next, enter the units from the density into the right side of the density table.

49.7 lbs1 Tm3

2. Find the volume of a substance whose density is 49.7 lbs/Tm3 and mass is 204,900 ng?

204,900 ng = ? Tm3

= ? lbs

D =

MV

If a conversion is necessary, complete it now.

0.006921 lbs1 Tm3


204,900 ng = ? Tm3

= ? lbs

204,900 ng = ?? lbs

Start with what you are looking for!!

lbs

Since lbs is an English unit and the given, ng, is a metric unit, Ms. Mullins must provide an English

to metric conversion. Always look back at the instructions to find the conversions. Use:

1 lb = 453.59 g

g1

453.59

204,900 ng = ?? lbs

Bring the denominator unit up to the next numerator.

1 lb

453.59 g

g

204,900 ng = ?? lbs

Convert grams to nanograms.

1 lb

453.59 g

g

ng

204,900 ng = ?? lbs

Since g is further left (so it is larger) than ng, g gets the one and ng gets the ten.

T _ _ G _ _ M _ _ k h da unit d c m _ _ μ _ _ n _ _ p

1 2 3 864 975

1 lb

453.59 g

g

ng

1

10 9

204,900 ng = ?? lbs


1 lb

453.59 g

g

ng

1

109

ng

When you have reached the given unit, ng, then insert the given numerical value.

204,900

204,900 ng = ?? lbs

1 lb

453.59 g

g

ng

1

109

ng 204,900

SOLVE!!

= 4.517 x 107 lbs

D =

MV

Enter the answer from the dimensional analysis into the density table.

49.7 lbs1 Tm3


204,900 ng = ? Tm3

= 4.517 x 107 lbs

D



V

M ÷

MD

xV =

D =

MV

Substitute the values into the equation.49.7 lbs

1 Tm3


204,900 ngTm3

V = M/DV = (4.517 x 107 lbs) / (49.7 lbs/Tm3)

= 4.517 x 107 lbs

D =

MV

Divide and round to the LEAST number of significant digits.

49.7 lbs1 Tm3


204,900 ngTm3

V = M/DV = (4.517 x 107 lbs) / (49.7 lbs/Tm3)

= 4.517 x 107 lbs

V = 2.24 x 105 Tm3

D =

MV


0.006921 lbs1 Tm3

3. Find the mass of a substance whose density is 0.006921 lbs/mm3 and volume is 7.0835 x 107 mi3?0.006921 lbs/Tm3 7.0835 x 107 mi3 ?

7.0835 x 107 mi3

D =

MV

Next, enter the units from the density into the right side of the density table.

0.006921 lbs1 Tm3

3. Find the mass of a substance whose density is 0.006921 lbs/Tm3 and volume is 7.0835 x 107 mi3?

7.0835 x 107 mi3 = ? Tm3

= ? lbs

D =

MV

If a conversion is necessary, complete it now.

0.006921 lbs1 Tm3


7.0835 x 107 mi3 = ? Tm3

= ? lbs

7.0835 x 107 mi3 = ?? Tm3

Start with what you are looking for!!

Tm3

Since Tm3 is a metric unit and the given, mi3, is an English unit, Ms. Mullins must provide an

English to metric conversion. Always look back at the instructions to find the conversions. Use:

1 m = 1.0936 yd

7.0835 x 107 mi3 = ?? Tm3

Tm3

However, the conversion is not a cubic conversion so.... 1 m = 1.0936 yd

(1 m)3 = (1.0936 yd)3

1 m3 = 1.3079 yd3

7.0835 x 107 mi3 = ?? Tm3

Tm3

In order to use the conversion, Tm3 must be converted to m3

7.0835 x 107 mi3 = ?? Tm3

Since Tm3 is further left (so it is larger) than m3, Tm3 gets the one and m3 gets the ten.

Tm3

m3

T _ _ G _ _ M _ _ k h da unit d c m _ _ μ _ _ n _ _ p

1

10

7.0835 x 107 mi3 = ?? Tm3

Either count by threes

Tm3

m3

T _ _ G _ _ M _ _ k h da unit d c m _ _ μ _ _

n _ _ p

1

10

3 6 9 3630241812 33272115

36

7.0835 x 107 mi3 = ?? Tm3

Or count between units and multiply by three.

Tm3

m3

T _ _ G _ _ M _ _ k h da unit d c m _ _ μ _ _

n _ _ p

1

10

1 2 3 1210864 11975

36

12 x 3 = 36

7.0835 x 107 mi3 = ?? Tm3


1 Tm3

1036 m3

m3

7.0835 x 107 mi3 = ?? Tm3

Now use the English to metric cubic conversion.

1 Tm3

1 m = 1.0936 yd(1 m)3 = (1.0936 yd)3

1 m3 = 1.3079 yd3

1036 m3

m31

1.3079 yd3

7.0835 x 107 mi3 = ?? Tm3


1 Tm3

1036 m3

m31

1.3079 yd3

yd3

7.0835 x 107 mi3 = ?? Tm3

Remember that you are working towards the given which is mi3.

1 Tm3

1036 m3

m31

1.3079 yd3

yd3

There isn’t a conversion between yards and miles, but there is between feet and miles, so first develop a

conversion between yd3 and ft3.1 yd = 3 ft

(1 yd)3 = (3 ft)3

1 yd3 = 27 ft3

ft327

1

7.0835 x 107 mi3 = ?? Tm3


1 Tm3

1036 m3

m31

1.3079 yd3

1 yd3

27 ft3

ft3

7.0835 x 107 mi3 = ?? Tm3

Remember that you are working towards the given which is mi3.

1 Tm3

1036 m3

m31

1.3079 yd3

yd3

There is a conversion between feet and miles, so first develop a conversion between ft3 and mi3.

5280 ft = 1 mi(5280 ft)3 = (1 mi)3

1.47 x 1011 ft3 = 1 mi3

ft3

27

1

ft3 mi3

1.47 x 1011

1

7.0835 x 107 mi3 = ?? Tm3


1 Tm3 1 m3 1 yd3 1.47 x 1011 ft3

1036 m3 1.3079 yd3 27 ft3 1 mi3 mi3

7.0835 x 107 mi3 = ?? Tm3

1 Tm3 1 m3 1 yd3 1.47 x 1011 ft3

1036 m3 1.3079 yd3 27 ft3 1 mi3 mi37.0835 x 107

When you have reached the given unit, mi3, then insert the given numerical value.

7.0835 x 107 mi3 = ?? Tm3

SOLVE!!1 Tm3 1 m3 1 yd3 1.47 x 1011 ft3

1036 m3 1.3079 yd3 27 ft3 1 mi3 mi37.0835 x 107

= 2.9487 x 1019 Tm3

D =

MV

Enter the answer from the dimensional analysis into the density table.

0.006921 lbs1 Tm3


7.0835 x 107 mi3 = 2.9487 x 1019

= ? lbsTm3

D



V

M ÷

M = DV

x

D =

MV

Substitute the values into the equation.0.006921 lbs

1 Tm3


7.0835 x 107 mi3 = 2.9487 x 1019

= ? lbsTm3

M = DV M = (0.006921 lbs/Tm3) (2.9487 x 1019 Tm3)

D =

MV

Multiply and round to the LEAST number of significant digits.

0.006921 lbs1 Tm3


7.0835 x 107 mi3 = 2.9487 x 1019

= ? lbsTm3

M = DV M = (0.006921 lbs/Tm3) (2.9487 x 1019 Tm3)

M = (2.041 x 1021 lbs)

Practice Problems:1. Find the mass of a substance whose density is 3.544 x 106 dg/yd3 and volume is 94,000 Mm3?2. Find the density of a substance whose mass is 1.87 x 106 cg and volume is 234,567 dam3?3. Find the volume of a substance whose density is 0.00807400 Gg/hm3 and mass is 204,900 tons?4. Find the mass of a substance whose density is 0.0007770 lbs/nL and volume is 4.7222 x 104 yd3?5. Find the density of a substance whose mass is 4.8 x 1028 kg and volume is 640,800 TL?6. Find the volume of a substance whose density is 3.04 x 1023 g/m3 and mass is 0.2030405 oz?

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Density Remediation