Question

How did you get `9.5%` for the theoretical yield of the potato chips in the Food Calorimetry Lab? I get `11%`.

Answer 1

Referring to this video:

It is a difference of rounding. If you do the actual earlier calculations and keep enough decimal places, you'll be starting with:

• `"34 g"` of potato chips in one serving
• `"9.6 calories"` in one potato chip
• `"1.75 g"` for each potato chip on average

Therefore, the calories per gram of potato chip is about:

`"9.6 Cal"/"1.75 g" = 5.4_(86)" Cal/g"`

where a subscript indicates the uncertain digits in our significant figures. This is actually where you should start noting that it's not precisely `"5.5 g"`.

On the food label Tyler gives, we see the `"34 g/serving"` conversion factor as a serving size, so:

`(34 cancel"g")/"serving" xx (5.4_(86)" Cal")/cancel"g" = 1.8_(651)xx10^2` `"Cal/serving"`

which rounds to `"190 Cal/serving"` as he got in the video. But notice the difference here in the percent error, which would be due to rounding to the `"5.5 g"` during the calculation.

`"% Error" = |"Actual" - "Theoretical"|/("Theoretical") xx 100%`

(His "actual" is actually our "theoretical", and his "measured" is our "actual")

`= |190 - 210|/(210)xx100% = color(red)(9.5%)` if you use `190`.

`= color(blue)(11._(19)%)` if you use `"186.51 Cal"` and then round.

Tyler wasn't wrong; he was just (implicitly?) saving all his digits in his calculator and rounding to the right significant figures for his audience.

So always save your rounding until the end to avoid differences like this.