Question

11. If a number is rounded to k decimal places, then
the absolute error is​

Answer 1

Step-by-step explanation:

Divide 9.1 by 7

We don't need to shift the decimal point at all, as the divisor (7) is already a whole number.

Ignore the decimal point in the dividend and use Long Division:

13

7)91

7

21

21

0

Put the decimal point in the answer directly above the decimal point in the dividend:

1.3

7)9.1

The answer is 1.3

Answer 2

Given: If a number is rounded to k decimal places

To find The absolute error is.

Solution: Absolute error due to rounding off to k digits.

               = | X – X′ | < 1/2 10n–k.

             and Relative error due to rounding off to k digits

               =  modulus of  X - X' / X  < ( 1/2(10 to power 1 -k)

Hence use the above formula for finding the absolute error