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Find the upper bound for the following length:

A) 18.7cm correct to 1 decimal place.
B) 58.37cm correct to 2 decimal places.

Please help.

Sagot :

Part A

Let's say we measure a board length and we measure 18.639 cm. Now let's say we round to the nearest tenth. That would lead to 18.6 cm. The question is "What is the largest value we can measure such that we round to the nearest tenth to get 18.7 cm?"

Well we could measure 18.7 cm exactly, but there are values we could measure that are larger to round to that value. We could measure 18.71 or 18.72, etc etc all the way up to 18.74; once we get to 18.75, it will round to 18.8

So this means that the largest we can measure is 18.74 and it is the upper bound we're after.

Answer: 18.74 cm

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Part B

We use the same idea as part A, but now we're extending out one more decimal place.

We could measure 58.37 cm exactly or we could measure 58.371 or we could do 58.372, etc until we arrive at 58.374

By the time we get to 58.375, it will round to 58.38 and that's not what we're after. So the highest we can go is 58.374 cm

Answer: 58.374 cm

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