Lesson 15Infinite Decimal Expansions
Learning Goal
Let’s think about infinite decimals.
Learning Targets
I can write a repeating decimal as a fraction.
I understand that every number has a decimal expansion.
Lesson Terms
- repeating decimal
Warm Up: Searching for Digits
Problem 1
The first 3 digits after the decimal for the decimal expansion of
Activity 1: Some Numbers Are Rational
Your teacher will give your group a set of cards. Each card will have a calculations side and an explanation side.
Problem 1
The cards show Noah’s work calculating the fraction representation of
Problem 2
Use Noah’s method to calculate the fraction representation of:
Are you ready for more?
Problem 1
Use this technique to find fractional representations for
Activity 2: Some Numbers Are Not Rational
Problem 1
Why is
between 1 and 2 on the number line? Why is
between 1.4 and 1.5 on the number line? How can you figure out an approximation for
accurate to 3 decimal places? Label all of the tick marks. Plot
on all three number lines. Make sure to add arrows from the second to the third number lines.
Problem 2
Elena notices a beaker in science class says it has a diameter of 9 cm and measures its circumference to be 28.3 cm. What value do you get for
using these values and the equation for circumference, ? Diego learned that one of the space shuttle fuel tanks had a diameter of 840 cm and a circumference of 2,639 cm. What value do you get for
using these values and the equation for circumference, ? Label all of the tick marks on the number lines. Use a calculator to get a very accurate approximation of
and plot that number on all three number lines. How can you explain the differences between these calculations of
?
Lesson Summary
Not every number is rational. Earlier we tried to find a fraction whose square is equal to 2. That turns out to be impossible, although we can get pretty close (try squaring
Any number, rational or irrational, has a decimal expansion. Sometimes it goes on forever. For example, the rational number