4.5.4.6 Absolute and Relative Errors

Question 1

Rounding Errors

Answer 1

Some decimal numbers cannot be represented exactly in binary even with fixed point or floating point, some numbers only can be approximately represented.
For this reason floating point and fixed point may be inaccurate

Question 2

Absolute Error

Answer 2

The actual amount by which the value is inaccurate, calculated by finding the difference between the given and actual value.

Question 3

Relative Error

Answer 3

Measure of uncertainty in given value compared to actual value relative to size of given value.

Question 4

Relative Error Formula

Answer 4

~ relative error = absolute error/actual value

~ can give a percentage when x by 100

Question 5

Relative Error Example

Answer 5

12.4 is represented in fixed point binary as 1100.011 calculate relative error as percentage to 4 S.F
~ 0.025 /12.4 x 100 = 0.2016

Question 6

Absolute Error Example

Answer 6

14.6 is represented as 1110.1 in binary calculate the absolute error
~ 14.6 - 14.5 = 0.1

Question 7

Errors in relation to magnitude

Answer 7

Absolute error of 0.1cm in 50cm is a very small relative error of 0.002% same absolute error of 0.1cm in 1cm is a much larger relative error of 10%