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IM 8.8.14 Lesson: Decimal Representations of Rational Numbers

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

What do you notice? What do you wonder?

Here is a number line from 0 to 1. Mark the midpoint between 0 and 1.

What is the decimal representation of that number?

Mark the midpoint between 0 and the newest point. What is the decimal representation of that number?

Repeat step two. How did you find the value of this number?

Describe how the value of the midpoints you have added to the number line keep changing as you find more. How do the decimal representations change? 

Rational numbers are fractions and their opposites. All of these numbers are rational numbers.

On the topmost number line, label the tick marks.

All rational numbers have decimal representations, too. Find the decimal representation of each of these rational numbers.

  • Next, find the first decimal place of  using long division and estimate where  should be placed on the top number line.
  • Label the tick marks of the second number line. Find the next decimal place of   by continuing the long division and estimate where   should be placed on the second number line. Add arrows from the second to the third number line to zoom in on the location of .
  • Repeat the earlier step for the remaining number lines.
 What do you think the decimal expansion of  is?

Let and . For each of the following questions, first decide whether the fraction or decimal representations of the numbers are more helpful to answer the question, and then find the answer. Which of  or  is closer to 2?

Find .

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