Show that $1\text{ cal/g}\cdot {\text{C}}^{\circ }=1\text{ kcal/kg}\cdot {\text{C}}^{\circ }$

Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to show that 1 calorie per gram Celsius degree equals 1 kilocalorie per kilogram Celsius degree. So the kilogram, the prefix 'kilo' means multiply by 10 to the 3 so we can replace kilocalorie with 1 times 10 to the 3 calories and the kilogram can be replaced with 1 times 10 to the 3 grams. This 1 times 10 to the 3 cancels on top and bottom and we are left with 1 calorie per gram per Celsius degree and so it's the same as this and there we go!