Comparing irrational numbers with a calculator

The  exercise appears under the 8th Grade Math Mission. This exercise gives a geometric and algebraic understanding of the location of irrational numbers.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the upper and lower bounds: This problem provides an irrational number not in decimal form. The student is asked to find an upper and lower bound of varying accuracy.Ain1.png
 * 2) Put in order: This problem provides a couple rational numbers and an irrational number. The student is asked to put the numbers in increasing order without using a calculator.Ain2.png
 * 3) Pick the point: This problem provides an irrational number and a couple points on a number line. The student is asked to select which of the pictured points is closest to the irrational number.Ain3.png

Strategies
Fast estimation techniques or memorization can help on this problem. Unfortunately, so can a calculator, although this is encouraged against in the instructions.
 * 1) Read carefully, the "Find the upper and lower bounds" problem sometimes asks integers and sometimes asks for higher accuracy.

Real-life applications

 * 1) Knowing the approximate decimal values for irrational numbers can help with a plethora of scientific applications.