# Question #cabd7

Jan 29, 2015

Since $1 l b = 454 g$ and $1 f t = 30.5 c m$ you have all the convertion ratios you need.
Also remember that $1 m L = 1 c {m}^{3}$

$65 l b = 65 \cdot 454 g = 29510 g$

$1 f {t}^{3} = {\left(30.5 c m\right)}^{3} = 28373 c {m}^{3}$ (cubic measures!)

Divide:

$\frac{65 l b}{f {t}^{3}} = \frac{29510 g}{28373 c {m}^{3}} = 1.040 g / c {m}^{3} = 1.040 g / m L$

Extra : Of course you could have worked out a conversion factor for any number, when going from $l b / f {t}^{3} \to g / m L$

This would work out (see above):

$\frac{1 l b}{f} {t}^{3} = \frac{454 g}{28373 c {m}^{3}} = 0.01600 g / m L$

Or (other way around) $1 g / m L = 62.496 l b / f {t}^{3}$

Jan 29, 2015

Every time you're dealing with unit conversions you must think conversion factors. Conversion factors will help you go either from one unit of measurement to another, or from one multiple to another.

In your example, you must convert ${\text{65 lbs/ft}}^{3}$ into $\text{g/mL}$ by converting $\text{lbs}$ into $\text{grams}$ and ${\text{ft}}^{3}$ into $\text{mL}$. The conversion factors for going from SI units to US customary units will usually be given to you. In this case, you have

$\text{1 lbs" = "0.4536 kg}$ and ${\text{1 ft"^3 = "0.02832 m}}^{3}$

You will be however expected to know that $\text{1 kg" = "1000 g}$, ${\text{1 m"^3 = "1,000,000 cm}}^{3}$, and $\text{1 cm"^3 = "1 mL}$. So, let's set up the conversion factors one by one

$65 \text{lbs"/"ft"^3 * ("0.4536 kg")/("1 lbs") * ("1000 g")/("1 kg") * ("1 ft"^3)/("0.02832 m"^3) * ("1 m"^3)/("1,000,000 cm"^3) * ("1 cm"^3)/("1 mL") = "1.04 g/mL}$

The successive conversion factors will get you from

$\text{lbs"/"ft"^3 -> "kg"/"ft"^3 -> "g"/"ft"^3 -> "g"/"m"^3 -> "g"/"cm"^3 -> "g"/"mL}$

This is just one way of going from ${\text{lbs/ft}}^{3}$ to $\text{g/mL}$. You can use any order you want, you can skip steps; for example, you can go from $\text{lbs}$ directly to $\text{g}$ without going to $\text{kg}$ first, and so on.