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Number and Operations Session 7, Part A: Fractions to Decimals
 
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Session 7, Part A:
Fractions to Decimals

In This Part: Terminating Decimals | Repeating Decimals | Repeating Decimal Rings

Here's another interesting phenomenon of repeating decimals.

We've explored repeating patterns for decimal expansions of such fractions as 1/7 (or other fractions with prime denominators larger than 7). What happens when the numerator is larger than 1? If you know the decimal representation of 1/7, is there an easy way to find the decimal representation of, say, 2/7?

One way would be to multiply the digits of the repeating part by 2. When we display the repeating parts in one or two rings, some interesting patterns emerge.

Problem A16

Solution  

a. 

Arrange the digits for one period of the repeating decimal expansion for 1/7 in a circle. Now find the decimal expansions for 2/7, 3/7, ..., and 6/7. How are 1/7 and 6/7 related? How are 2/7 and 5/7 related? How about 3/7 and 4/7?

b. 

You might try thinking that 7 has one ring and that the size of the ring is six. Try the same idea with the number 13. How would you describe 13?

c. 

Explore this idea with other prime numbers.


Next > Part B: Decimals to Fractions

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