Question

If the true value of a quantity is 2.3 and the absolute error must be less than ​0.06, find the acceptable measured values.

Answer 1

Answer: 2.24 < x < 2.36

x is between 2.24 and 2.36, excluding the endpoints

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Work Shown:

x = measured value

T = target or true value = 2.3

E = error = 0.06

The inequality we want to solve is in the form |x-T| < E

Plugging in the given T and E values leads to |x-2.3| < 0.06

Now use the idea if |x| < k, for some positive value k, then -k < x < k.

So,

|x-2.3| < 0.06

-0.06 < x-2.3 < 0.06

-0.06+2.3 < x-2.3+2.3 < 0.06+2.3

2.24 < x+0 < 2.36

2.24 < x < 2.36

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A thing to notice is that if the measured value is x = 2.36, then the error is

|x-T| = |2.36-2.3| = |0.06| = 0.06

or if the measured value is x = 2.24, we get an error of

|x-T| = |2.24-2.3| = |-0.06| = 0.06

So we can see the absolute value is to ensure the difference isn't negative.

As long as x is between 2.24 and 2.36, excluding the endpoints, then the error will be less than 0.06