Math / Numbers & Operations

Question $3.20 \mathrm{~g} / \mathrm{cm}^{3} \rightarrow \mathrm{~kg} / \mathrm{m}^{3}$

Studdy Solution

STEP 1

What is this asking? We need to convert a density from grams per cubic centimeter to kilograms per cubic meter. Watch out! Remember those metric prefixes!
A kilogram is 1000 grams, and a meter is 100 centimeters.
Don't mix them up!

STEP 2

1. Convert grams to kilograms.
2. Convert cubic centimeters to cubic meters.
3. Combine the conversions.

STEP 3

We're starting with a density of $3.20 \mathrm{~g}/\mathrm{cm}^3$ .
We want to convert the grams to kilograms.
Remember that there are $1000$ grams in $1$ kilogram.

STEP 4

To convert, we'll multiply by a clever fraction that's equal to one!
We'll put kilograms on top and grams on the bottom: $\frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}$ .
Since $1 \mathrm{~kg}$ is the same as $1000 \mathrm{~g}$ , this fraction is just a fancy way of writing the number one!

STEP 5

So, we have $3.20 \frac{\mathrm{g}}{\mathrm{cm}^3} \cdot \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}$ .
Notice how the grams add to zero!
This leaves us with $0.00320 \frac{\mathrm{kg}}{\mathrm{cm}^3}$ .
Awesome!

STEP 6

Now, let's tackle those cubic centimeters.
There are $100$ centimeters in $1$ meter.
But we're dealing with cubic centimeters and cubic meters, so we need to cube the conversion factor!

STEP 7

This gives us $(100 \mathrm{~cm})^3 = (1 \mathrm{~m})^3$ , which simplifies to $1,000,000 \mathrm{~cm}^3 = 1 \mathrm{~m}^3$ .
So, there are one million cubic centimeters in a cubic meter!

STEP 8

Again, we'll multiply by a fraction equal to one, with cubic meters on top and cubic centimeters on the bottom: $\frac{1 \mathrm{~m}^3}{1,000,000 \mathrm{~cm}^3}$ .

STEP 9

Multiplying our previous result, we get $0.00320 \frac{\mathrm{kg}}{\mathrm{cm}^3} \cdot \frac{1 \mathrm{~m}^3}{1,000,000 \mathrm{~cm}^3}$ .
The cubic centimeters add to zero, leaving us with $0.0000000032 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .
We're almost there!

STEP 10

Let's make this number look a little nicer.
We can rewrite $0.0000000032$ in scientific notation as $3.20 \cdot 10^{-9}$ .

STEP 11

We can also express this as $3.20 \cdot 10^{-9} \cdot 10^6 \cdot 10^3 = 3.20 \cdot 10^0 = 3.20 \cdot 1 = 3200$ .
So, our final answer is $3200 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .

STEP 12

The density is $3200 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .

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Question $3.20 \mathrm{~g} / \mathrm{cm}^{3} \rightarrow \mathrm{~kg} / \mathrm{m}^{3}$

Studdy Solution

STEP 1

What is this asking? We need to convert a density from grams per cubic centimeter to kilograms per cubic meter. Watch out! Remember those metric prefixes!
A kilogram is 1000 grams, and a meter is 100 centimeters.
Don't mix them up!

STEP 2

1. Convert grams to kilograms.
2. Convert cubic centimeters to cubic meters.
3. Combine the conversions.

STEP 3

We're starting with a density of $3.20 \mathrm{~g}/\mathrm{cm}^3$ .
We want to convert the grams to kilograms.
Remember that there are $1000$ grams in $1$ kilogram.

STEP 4

To convert, we'll multiply by a clever fraction that's equal to one!
We'll put kilograms on top and grams on the bottom: $\frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}$ .
Since $1 \mathrm{~kg}$ is the same as $1000 \mathrm{~g}$ , this fraction is just a fancy way of writing the number one!

STEP 5

So, we have $3.20 \frac{\mathrm{g}}{\mathrm{cm}^3} \cdot \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}$ .
Notice how the grams add to zero!
This leaves us with $0.00320 \frac{\mathrm{kg}}{\mathrm{cm}^3}$ .
Awesome!

STEP 6

Now, let's tackle those cubic centimeters.
There are $100$ centimeters in $1$ meter.
But we're dealing with cubic centimeters and cubic meters, so we need to cube the conversion factor!

STEP 7

This gives us $(100 \mathrm{~cm})^3 = (1 \mathrm{~m})^3$ , which simplifies to $1,000,000 \mathrm{~cm}^3 = 1 \mathrm{~m}^3$ .
So, there are one million cubic centimeters in a cubic meter!

STEP 8

Again, we'll multiply by a fraction equal to one, with cubic meters on top and cubic centimeters on the bottom: $\frac{1 \mathrm{~m}^3}{1,000,000 \mathrm{~cm}^3}$ .

STEP 9

Multiplying our previous result, we get $0.00320 \frac{\mathrm{kg}}{\mathrm{cm}^3} \cdot \frac{1 \mathrm{~m}^3}{1,000,000 \mathrm{~cm}^3}$ .
The cubic centimeters add to zero, leaving us with $0.0000000032 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .
We're almost there!

STEP 10

Let's make this number look a little nicer.
We can rewrite $0.0000000032$ in scientific notation as $3.20 \cdot 10^{-9}$ .

STEP 11

We can also express this as $3.20 \cdot 10^{-9} \cdot 10^6 \cdot 10^3 = 3.20 \cdot 10^0 = 3.20 \cdot 1 = 3200$ .
So, our final answer is $3200 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .

STEP 12

The density is $3200 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .

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Question3.20 g/cm3→ kg/m33.20 \mathrm{~g} / \mathrm{cm}^{3} \rightarrow \mathrm{~kg} / \mathrm{m}^{3}3.20 g/cm3→ kg/m3

Studdy Solution

STEP 1

What is this asking? We need to convert a density from grams per cubic centimeter to kilograms per cubic meter. Watch out! Remember those metric prefixes!A kilogram is 1000 grams, and a meter is 100 centimeters.Don't mix them up!

STEP 2

1. Convert grams to kilograms.2. Convert cubic centimeters to cubic meters.3. Combine the conversions.

STEP 3

We're starting with a density of 3.20 g/cm33.20 \mathrm{~g}/\mathrm{cm}^33.20 g/cm3.We want to **convert** the grams to kilograms.Remember that there are 100010001000 grams in 111 kilogram.

STEP 4

STEP 5

So, we have 3.20gcm3⋅1 kg1000 g3.20 \frac{\mathrm{g}}{\mathrm{cm}^3} \cdot \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}3.20cm3g​⋅1000 g1 kg​.Notice how the grams **add to zero**!This leaves us with 0.00320kgcm30.00320 \frac{\mathrm{kg}}{\mathrm{cm}^3}0.00320cm3kg​.Awesome!

STEP 6

Now, let's tackle those cubic centimeters.There are 100100100 centimeters in 111 meter.But we're dealing with *cubic* centimeters and *cubic* meters, so we need to **cube** the conversion factor!

STEP 7

This gives us (100 cm)3=(1 m)3(100 \mathrm{~cm})^3 = (1 \mathrm{~m})^3(100 cm)3=(1 m)3, which simplifies to 1,000,000 cm3=1 m31,000,000 \mathrm{~cm}^3 = 1 \mathrm{~m}^31,000,000 cm3=1 m3.So, there are **one million** cubic centimeters in a cubic meter!

STEP 8

Again, we'll **multiply** by a fraction equal to one, with cubic meters on top and cubic centimeters on the bottom: 1 m31,000,000 cm3\frac{1 \mathrm{~m}^3}{1,000,000 \mathrm{~cm}^3}1,000,000 cm31 m3​.

STEP 9

STEP 10

Let's make this number look a little nicer.We can **rewrite** 0.00000000320.00000000320.0000000032 in scientific notation as 3.20⋅10−93.20 \cdot 10^{-9}3.20⋅10−9.

STEP 11

We can also express this as 3.20⋅10−9⋅106⋅103=3.20⋅100=3.20⋅1=32003.20 \cdot 10^{-9} \cdot 10^6 \cdot 10^3 = 3.20 \cdot 10^0 = 3.20 \cdot 1 = 32003.20⋅10−9⋅106⋅103=3.20⋅100=3.20⋅1=3200.So, our **final answer** is 3200kgm33200 \frac{\mathrm{kg}}{\mathrm{m}^3}3200m3kg​.

STEP 12

The density is 3200kgm33200 \frac{\mathrm{kg}}{\mathrm{m}^3}3200m3kg​.

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Studdy solves anything!

Start learning now

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Question $3.20 \mathrm{~g} / \mathrm{cm}^{3} \rightarrow \mathrm{~kg} / \mathrm{m}^{3}$

What is this asking? We need to convert a density from grams per cubic centimeter to kilograms per cubic meter. Watch out! Remember those metric prefixes!
A kilogram is 1000 grams, and a meter is 100 centimeters.
Don't mix them up!

1. Convert grams to kilograms.
2. Convert cubic centimeters to cubic meters.
3. Combine the conversions.

We're starting with a density of $3.20 \mathrm{~g}/\mathrm{cm}^3$ .
We want to convert the grams to kilograms.
Remember that there are $1000$ grams in $1$ kilogram.

So, we have $3.20 \frac{\mathrm{g}}{\mathrm{cm}^3} \cdot \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}$ .
Notice how the grams add to zero!
This leaves us with $0.00320 \frac{\mathrm{kg}}{\mathrm{cm}^3}$ .
Awesome!

Now, let's tackle those cubic centimeters.
There are $100$ centimeters in $1$ meter.
But we're dealing with cubic centimeters and cubic meters, so we need to cube the conversion factor!

This gives us $(100 \mathrm{~cm})^3 = (1 \mathrm{~m})^3$ , which simplifies to $1,000,000 \mathrm{~cm}^3 = 1 \mathrm{~m}^3$ .
So, there are one million cubic centimeters in a cubic meter!

Again, we'll multiply by a fraction equal to one, with cubic meters on top and cubic centimeters on the bottom: $\frac{1 \mathrm{~m}^3}{1,000,000 \mathrm{~cm}^3}$ .

Let's make this number look a little nicer.
We can rewrite $0.0000000032$ in scientific notation as $3.20 \cdot 10^{-9}$ .

We can also express this as $3.20 \cdot 10^{-9} \cdot 10^6 \cdot 10^3 = 3.20 \cdot 10^0 = 3.20 \cdot 1 = 3200$ .
So, our final answer is $3200 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .

The density is $3200 \frac{\mathrm{kg}}{\mathrm{m}^3}$ .