# How do you convert 3.345 kilojoules to millijoules ?

## Question:

How do you convert {eq}3.345 \ kilojoules {/eq} to {eq}millijoules {/eq} ?

## Joule:

The Joule (J) is the SI unit of energy. One joule is equal to one kilogram meter squared per second squared {eq}\displaystyle (1\ J = 1\ kg\ m^2 /s^2) {/eq}. Joule is used in expressing kinetic energies, potential energies, and anything else that counts as such. Joules are also used as units of heat, since heat is basically a transfer in thermal energy.

Given:

• {eq}\displaystyle Q = 3.345\ kJ {/eq} is the heat

Let us recall the following relations between joules:

• {eq}\displaystyle 1\ kJ = 1000\ J {/eq}
• {eq}\displaystyle 1\ J = 1000\ mJ {/eq}

So here what we want to do is cancel out the kJ unit and leave out the mJ unit which is currently nowhere to be found. We can make it appear by using conversion:

{eq}\displaystyle Q = 3.345\ kJ \left(\frac{1000\ J}{1\ kJ} \right)\left(\frac{1000\ mJ}{1\ J} \right) {/eq}

These fractions are valid because we have assigned them to be equal. They are thus equal to 1 and as we know, multiplying a number by 1 equals itself. We could thus cancel out unwanted units here:

{eq}\displaystyle Q = 3.345\ \require{cancel}\cancel{kJ} \left(\frac{1000\ \require{cancel}\cancel{J}}{1\ \require{cancel}\cancel{kJ}} \right)\left(\frac{1000\ mJ}{1\ \require{cancel}\cancel{J}} \right) {/eq}

We thus get:

{eq}\displaystyle \boxed{Q = 3,345,000\ mJ} {/eq}