| Comparing irrational numbers with a calculator | |
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| 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:
- 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.
Find the upper and lower bounds
- 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.
Put in order
- 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.
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.
- Read carefully, the "Find the upper and lower bounds" problem sometimes asks integers and sometimes asks for higher accuracy.
Real-life Applications[]
- Knowing the approximate decimal values for irrational numbers can help with a plethora of scientific applications.
- 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!