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Question

A copper wire is to have a length of 16 cm with a tolerance of ± 0.02 cm. How much must be trimmed from a wire that is 18 cm long for it to meet specifications?

at least 1.75 cm and no more than 2.25 cm

at least 1.89 cm and no more than 2.20 cm

at least 1.90 cm and no more than 2.10 cm

at least 1.98 cm and no more than 2.02 cm

Can you explain this question to me?

Answer 1

"at least 1.98 cm and no more than 2.02 cm" is correct.

Tolerance of ± 0.02 cm means that the trimmed length is good if differs from 16 cm by .02 cm or less. If can be .02 cm MORE than 16 cm, or .02 cm LESS than 16 cm and it will still be "within tolerance".

.02 cm more is 16.02 cm.  .02 cm less is 15.98 cm.  So the acceptable cut length is from 15.98 to 16.02.  therefore you can cut 1.98 cm off of 18 cm to get to the long end of the tolerance, or you can cut off 2.02 cm to get to the short end.

Simpler put, you need to trim off exactly 2 cm to make it perfect (18 minus 16).  But it doesn't need to be perfect, it can be off by .02 cm in either direction.  2 cm of cut minus .02 cm is 1.98 cm.  2 cm of cut plus .02 cm is 2.02 cm.  So you need cut off between 1.98 and 2.02 cm.

Answer 2

16 cm with a tolerance of +/- 0.02 cm means the length of the wire should be between 15.98 cm and 16.02 cm

Hence, the trimming from a 18cm wire must be

atleast 1.98 cm and at most 2.02 cm

Answer 3

at least 1.98 cm and no more than 2.02 cm