Question

The length of an object is exactly 20 centimeters. A student says that a measurement of 19 centimeters represents a percent error of 95%, while a measurement of 21 centimeters represents a percent error of 105%. Explain what the student did wrong. What are the correct percent errors?

Answer 1

95 percent of 20 is 19cm... so that's correct
however a percent error of 95 for 20 would mean plus or minus 19 cm... so if the length was 20 and the student measured it as the length is 1cm, they would have a 95 percent error
what they actually had was a 5 percent error: the length of the object is 20cm and they measured it as 19cm, so their measurements were 1cm off
1/20 = 0.05 = 5%

Answer 2

same again for the 21cm measurement
length = 20
measured length = 21
difference = 1cm
so percent error = 1/20 = 0.05 = 5%
if you need to assign positive and negative values to it,
the 19cm measurement was -5% error
the 21cm measurement was +5% error

Answer 3

does that make sense @bblahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh ??