Answer: (a) To approximate , we are going to use a compass to draw a cirle of radius 2 and circumference 12.5. Remember that is the ratio between the circumference of a circle and its diameter; since the diameter of a circle is two times its radius, we can find using the equation:
Infinity= 3.1
And to the nearest tenth:
Step-by-step explanation: To approximate , we are going to use the Babylonian method:
Step 1. We are going to make a guess. Our guess is 2 because , so must be close to 2.
Step 2. We are going to divide 5 by 2:
Step 3. We are going to find the average between our initial guest and the result of our previous calculation:
And to the nearest tenth:
To approximate , we are going to use the Babylonian method one more time:
Step 1. Our guess is 3 because , so must be close to 3.
Step 2. We are going to divide 8 by 3:
Step 3. We are going to find the average between our initial guest and the result of our previous calculation:
To approximate we are going to multiply our approximation of and multiply it by 2:
(b) Since we have our irrational numbers expressed as decimal approximations, we can compare them to arrange them form least to greatest:
2.2,2.8,3.1,4.4
Now, we just need to replace the decimal approximations with the original numbers:
,,,
We can conclude that ordering the ribbon sizes from least to greatest we get:
,,,
