Question

A length is measured as 21cm correct to 2 significant figures. what is the upper bound for the length?​

Answer 1

the upper bound for the length is  $21.5 cm$ .

Step-by-step explanation:

Lower and Upper Bounds

• The lower bound is the smallest value that will round up to the approximate value.
• The upper bound is the smallest value that will round up to the next approximate value.

Ex:- a mass of 70 kg, rounded to the nearest 10 kg, The upper bound is 75 kg, because 75 kg is the smallest mass that would round up to 80kg.

Here , A length is measured as 21cm correct to 2 significant figures. We need to find what is the upper bound for the length . let's find out:

As discussed above , upper bound for any number will be the smallest value in decimals which will round up to next integer value . So , for 21 :

⇒ $21.5 cm$

21.5 cm on rounding off will give 22 cm . So , the upper bound for the length is  $21.5 cm$ .

Answer 2

The question is an illustration of approximation and estimation.

The upper bound for the length is 21.4 cm

The approximated length to 2 significant digits is given as:

$\mathbf{Length = 21cm}$

The smallest number that approximates to 21 is 20.5, while the highest is 21.4...

This means that:

Lower bound = 20.5

Upper bound = 21.4

Hence, the upper bound for the length is 21.4 cm

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