# 30 - Absolute and Relative Errors

1. If the correct answer is 100 and it is stored as 100.9, that is not too far off. However, 1.9 is a long way from an answer of 1.0. The latter presents a greater error.

TRUE

FALSE

2. If we denote the correct answer as 'x' and the stored value as 'x0', then the absolute error is simply ______________

x - x0

x - x/x0

x + x0

x/x0+x0/x

3. In the following example, what is the absolute error in both cases?
```Example 1:
==========
Stored number: 1.9

Example 2:
==========
Stored number: 100.9

None of the above

In example one the error is 0.9 and in example two the error is 100.

In both examples the error is 0.9

In both examples the error is a factor of 1 i.e 1.

4. It is critical to see what the error is in relation to _______________________

how large the number is

how many bits are in the number

the value of the number (especially if it is very small)

None of the above

5. The actual number difference beween the desired value and the rounded value is called the ___________________________

absolute error

marginal error

relative error

floating error

6. The percentage difference between the desired value and the rounded value is called the ___________________

relative error

absolute error

floating error

marginal error

7. In the following example, fill in the blanks for 1. and 2. 1. relative error 2. absolute error

1. absolute error 2. relative error

None of these options apply

Both 1 and 2 are different ways of representing the absolute error

8. For example, if p = 0.4 and p? = 0.404, the absolute error in the approximation is:

9. If p = 0.4 and p? = 0.404, the relative error in the approximation is:

10. Using 8 bit fixed point unsigned fraction with 4 bits for the decimal points: Is the calculation shown to find the absolute error trying to represent 8.8 correct? (True or False?)
```1000.1101
8.8 - 8.8125 = 0.0125
(0.0125/8.8) * 100 = 0.14%```

FALSE

TRUE

11. Errors, especially rounding errors, can have deadly consequences. e.g. the 1991 patriot missile misses scud and 1996 - Ariane rocket explodes!

FALSE

TRUE

12. An absolute error could also be be described as the approximate value - true value.

FALSE

TRUE

13. The relative error is the absolute error/absolute error +1 1 * 100

TRUE

FALSE

14. Some people tend to use the term accuracy when speaking of absolute errors and the term precision when speaking of relative errors

FALSE

TRUE

15. What is the absolute error? Refer to the image below. Answer: 11111110000 000101 (–5 – 234 = –33)

Answer: 0.025 / -0.025 / 6.9-6.875 / 1/40

None of the above

Answer: 0.00362319 / 0.025/6.9 / 1/276 = 0.362319%