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Edit: Engineers, inventors, etc. take scientific principles and apply them to current scientific principles and technologies to solve everyday problems, and in the process, develop new technologies.

For example, if we didn’t have chemistry, and physics (science) we may not know how to make our own fire (technology). But thanks to science, we know that friction can cause heat, and we also know that oxygen fuels a fire, so now we can rely on fires to keep us warm. But as scientific principles develop, technologies can further develop (always relying on existing scientific principles), so that now, we have radiators to keep us warm! A lot safer than fires!

This is how technology relates to science; science forms a basis for technology, (i.e. technology uses science). Without science, technology would not exist.