Show that 1 cal/gC=1 kcal/kgC1 \textrm{ cal/g}\cdot\textrm{C}^\circ = 1\textrm{ kcal/kg}\cdot\textrm{C}^\circ
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OpenStax College Physics for AP® Courses, Chapter 14, Problem 2 (Problems & Exercises)

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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!