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Comparing irrational numbers with a calculator
Square roots 2 256
Description
Exercise Name: Comparing irrational numbers with a calculator
Math Missions: 8th grade (U.S.) Math Mission, Pre-algebra Math Mission
Types of Problems: 3

The Comparing irrational numbers with a calculator exercise appears under the 8th grade (U.S.) Math Mission and Pre-algebra 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. Users are asked to find an upper and lower bound of varying accuracy.
    Ain1

    Find the upper and lower bounds

  2. Put in order: This problem provides a couple rational numbers and an irrational number. The user is asked to put the numbers in increasing order without using a calculator.
    Ain2

    Put in order

  3. Pick the point: This problem provides an irrational number and a couple points on a number line. The user is asked to select which of the pictured points is closest to the irrational number.
    Ain3

    Pick the point

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.
  2. Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers!

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