# Question eb202

Jun 20, 2017

${\text{2.51 g/cm"^3 = "5.53 lb/L" = 2.51 × 10^3color(white)(l) "kg/m}}^{3}$

#### Explanation:

${\text{g/cm}}^{3}$ to $\text{lb/L}$

Let's do the conversion one step at a time using familiar conversion factors.

We know that 1 lb = 453.6 g.

(2.51 color(red)(cancel(color(black)("g"))))/("1 cm"^3) × "1 lb"/(453.6 color(red)(cancel(color(black)("g")))) = 5.534 × 10^"-3" color(white)(l)"lb/cm"^3

We know that $\text{1000 cm"^3 = "1 L}$.

(5.534 × 10^"-3"color(white)(l) "lb")/(1 color(red)(cancel(color(black)("cm"^3)))) × (1000 color(red)(cancel(color(black)("cm"^3))))/"1 L" = "5.53 lb/L"

${\text{g/cm}}^{3}$ to ${\text{kg/m}}^{3}$

We know that 1 kg = 1000 g.

(2.51 color(red)(cancel(color(black)("g"))))/("1 cm"^3) × "1 kg"/(1000 color(red)(cancel(color(black)("g")))) = 2.51 × 10^"-3"color(white)(l) "kg/cm"^3

We know that 1 m = 100 cm.

${\left(\text{1 m")^3 = ("100 cm}\right)}^{3}$

or

${\text{1 m"^3 = 10^6color(white)(l) "cm}}^{3}$

(2.51 × 10^"-3"color(white)(l) "kg")/(1 color(red)(cancel(color(black)("cm"^3)))) × (10^6 color(red)(cancel(color(black)("cm"^3))))/("1 m"^3) = 2.51 × 10^3 color(white)(l)"kg/m"^3#