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

##### 1 Answer

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

On the food label Tyler gives, we see the

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

which rounds to

#"% 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"# andthenround.

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.**