In high school, some students have been confused to believe that 22/7 is already the actual value of π or an acceptable approximation. show that 355/113 is a better approximation in terms of absolute and relative errors.

Since it has smaller absolute and relative errors, 355/113 is a better aproximation for than 22/7

Step-by-step explanation:

The formula for the absolute error is:

Absolute error = |Actual Value - Measured Value|

The formula for the relative error is:

Relative error = |Absolute error/Actual value|

I am going to consider the actual value of as 3.14159265359.

In the case of 22/7:

22/7 = 3.14285714286.

Absolute error = |3.14159265359 - 3.14285714286| = 0.00126448927

Relative error = 0.00126448927/3.14159265359 = 0.00040249943 = 0.04%

In the case of 355/113

355/113 = 3.14159292035

Absolute error = |3.14159265359 - 3.14159292035| = 0.00000026676

Relative error = 0.00000026676/3.14159265359 = 0.000000085 = 0.0000085%

Since it has smaller absolute and relative errors, 355/113 is a better aproximation for than 22/7

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}