Question

Evaluate the sum = √3 + √5 + √7 to four significant digits and find its absolute and relative errors

Answer 1

Answer:

This presentation contains a brief description about floating point numbers and their representation and arithmetic, types of error (absolute error, relative error)

Step-by-step explanation:

This presentation contains the solution of previous year questions of MCSE-004 .

Answer 2

GIVEN,

√3+√5+√7

TO FIND,

sum of given expression, absolute and relative error.

SOLUTION,

as we know, the values of

√3- 1.73205

√5- 2.23606

√7- 2.64575

hence the sum is = 1.732+ 2.236+ 2.645 ( upto 4 significant figures)

                            = 6.613

                            ≈ 6.6

The difference between the measured or calculated value of a quantity and its actual or real value is called absolute error.

absolute error= real value- approximate value

                         =6.613-6.6

                         = 0.013

Relative error when used as a measure of precision is the ratio of the absolute error of a measurement to the calculated measurement.

relative error=$\frac{absolute error}{real value}$

                     =$\frac{0.013}{6.613}$

                     = 0.00196%

HENCE THE SUM IS 6.613, ABSOLUTE ERROR= 0.013, RELATIVE ERROR= 0.00196%.