1. Activating Prior Knowledge – Module Page 61
Use long division to find the decimal expansion of

2. Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Objective:
Today, we will develop and alternate method for computing the decimal expansion of a rational number.
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3. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
To start, let’s determine which two integers the fraction is between.
We know that is between 3 and 4 because = = ? ? ?
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4. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

5. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

6. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

7. Concept Development ? ? CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
So here’s what we have so far: = ? ?
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8. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

9. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

10. Concept Development ? CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
So now we have, = ?
CFU

11. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

12. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

13. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
CFU

14. Concept Development CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Concept Development
Module Pg. 61
Example 1 (revisited): Let’s see if we can come up with the decimal expansion of without using long division.
So the decimal expansion of to 3 decimal places is
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15. Guided Practice Exercise 1: CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Guided Practice
Module Pg. 62
Exercise 1:
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16. Guided Practice Exercise 1con’t: CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Guided Practice
Module Pg. 62
Exercise 1con’t:
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17. Guided Practice Exercise 1con’t: CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Guided Practice
Module Pg. 62
Exercise 1con’t:
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18. Guided Practice Exercise 2: CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Guided Practice
Module Pg. 62
Exercise 2:
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19. Guided Practice Exercise 2 con’t: CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Guided Practice
Module Pg. 62
Exercise 2 con’t:
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20. Guided Practice Exercise 2 con’t: CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Guided Practice
Module Pg. 62
Exercise 2 con’t:
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21. Guided Practice Exercise 2 con’t: CFU
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Guided Practice
Module Pg. 62
Exercise 2 con’t:
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22. Independent Practice –
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Independent Practice –
Module Pg. 62
Complete Exercise 3 with a partner (5 min):
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23. Independent Practice –
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Independent Practice –
Module Pg. 62
Complete Exercise 3 with a partner (5 min):
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24. Independent Practice –
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Independent Practice –
Module Pg. 62
Complete Exercise 3 with a partner (5 min):
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25. Independent Practice –
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Independent Practice –
Module Pg. 62
Complete Exercise 3 with a partner (5 min):
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26. Closure – Homework: Problem Set 1 – 5 page 64.
Module 7 Lesson 12: Decimal Expansions of Fractions, Part 2
Closure –
What did you learn?
Why is it important?
When comparing rational approximation to long division, what do you notice?
Homework:
Problem Set 1 – 5 page 64.
You must complete homework on a separate sheet of paper to receive credit.
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