# Question 45bf3

Jan 21, 2015

$\text{10 g" +- "1 g}$ represents a way bigger uncertainty than $\text{200 mL" +- "1 mL}$.

If you weigh something to be $\text{10 g" +- "1 g}$, the actual mass of the object cannot be smaller than $\text{10 g - 1g = 9 g}$, and bigger than $\text{10 g + 1 g = 11 g}$. This will give you a percent error of (you can use either measurement because the formula uses absolute value)

"% error" = | (10 - (10+-1))/10| * 100 = |(10-11)/10| * 100 = 10%

If you measure something to have $\text{200 mL" +- "1 mL}$, your value cannot be smaller than $\text{200 mL - 1 mL = 199 mL}$ and bigger than $\text{200 mL + 1 mL = 201 mL}$. In this case, the percent error will be

"% error" = |(200-(200+-1))/200|*100 = |(200-199)/200|*100 = 0.5%#

Since percent errors are best kept below $\text{5%}$, the measurement that produces a $\text{10%}$ error is not reliable at all; however, the measurement that produced a $\text{0.5%}$ error is considered to be very accurate.

You will definitely have greater uncertainty about the value you've measured in the case of the $\text{10 g" +- "1 g}$ measurement.