Question

Convert 5.78 kg/L to g/mL.

Answer 1

`5.78\; {\rm g\cdot mL^(-1)}`.

Step-by-step explanation:

This unit conversion can be achieved in the following steps:

• Convert from
  `{\rm kg\cdot L^(-1)}` to
  `{\rm g\cdot L^(-1)}`.
• Convert from
  `{\rm g\cdot L^(-1)}` to
  `{\rm g\cdot mL^(-1)}`.

In the given quantity, the mass of one liter of this material is
`5.78\; {\rm kg}`. One kilogram is equal to
`10^(3)\; {\rm g}`. Therefore, that
`5.78\; {\rm kg}\!` would be equivalent to
`5.78 * 10^(3)\; {\rm g} = 5780\; {\rm g}`.

Hence:

`\begin{aligned}& 5.78\; {\rm kg\cdot L^(-1)} \\ =\; & (5.78\; {\rm kg\cdot L^(-1)}) * \frac{10^(3)\; {\rm g}}{1\; {\rm kg}} \\ =\; & 5.78 * 10^(3)\; {\rm g\cdot L^(-1)}\end{aligned}`.

One milliliter is equivalent to one-thousandth of a liter:
`1\; {\rm mL} = 10^(-3)\; {\rm L}`. Thus, the mass of one
`{\rm mL}` of this given material would be one-thousandth of the mass of one
`{\rm L}` of this material:

`\begin{aligned}& 5.78 * 10^(3)\; {\rm g\cdot L^(-1)} \\ =\; & 5.78 * 10^(3)\; {\rm g\cdot L^(-1)}* \frac{1\; {\rm L}}{10^(3)\; {\rm mL}} \\ =\; & 5.78 \; {\rm g\cdot mL^(-1)}\end{aligned}`.

Hence,
`5.78\; {\rm kg\cdot L^(-1)}` would be equivalent to
`5.78\; {\rm g\cdot mL^(-1)}`.