Question

For a scale to pass inspection, the scale's reading can vary by at most0.1% from the actual mass of an object on the scale. A test mass hasan exact mass of 250.00 grams. In what range must the scale's readingbe for the scale to pass inspection?

Answer 1

Given that the reading can fluctuate by at most 0.1%.

The actual mass of the test element is given as 250.00 grams.

Then the upper limit (UL) of the range is calculated as,

$\begin{gathered} UL=250.00+0.1\text{ percent of }250.00 \\ UL=250.00+(\frac{0.1}{100}\times250.00) \\ UL=250.00+0.25 \\ UL=250.25 \end{gathered}$

And the lower limit (LL) of the range is calculated as,

$\begin{gathered} LL=250.00-0.1\text{ percent of }250.00 \\ LL=250.00-(\frac{0.1}{100}\times250.00) \\ LL=250.00-0.25 \\ LL=249.75 \end{gathered}$

Then the corresponding range R is given by,

$\begin{gathered} R=\lbrack LL,UL\rbrack \\ R=\lbrack249.75,250.25\rbrack \end{gathered}$

Thus, the range of scale's reading to pass the inspection is,

$\lbrack249.75,250.25\rbrack$