Question #45bf3

1 Answer
Jan 21, 2015

#"10 g" +- "1 g"# represents a way bigger uncertainty than #"200 mL" +- "1 mL"#.

If you weigh something to be #"10 g" +- "1 g"#, the actual mass of the object cannot be smaller than #"10 g - 1g = 9 g"#, and bigger than #"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 #"200 mL" +- "1 mL"#, your value cannot be smaller than #"200 mL - 1 mL = 199 mL"# and bigger than #"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 #"5%"#, the measurement that produces a #"10%"# error is not reliable at all; however, the measurement that produced a #"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 #"10 g" +- "1 g"# measurement.