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Cyclic Number

I got this activity from  Mental Math Workout by Michael Lobosco

142857  is a cyclic number.

1/7 = 0.142857142857

 Have a student roll a dice.  Have the class multiply 142857 by the number .

You can write the answer on the board.  For example if a 4 is rolled  you just multiply  4 and 7 .

The final digit in the answer is 8  so the complete answer is

571428

To add a little twist to this I took the activity from the Lobosco book.  I held up an envelope with the answer inside.  I had prepared a loop of paper and placed so that the flap of the envelope separates  142  and 857.   Using the example above I would cut the loop between 8 and 5 to give the answer 

571428

 

The last class I did this with had difficulty.  The number we rolled was 6  and only 4 students in the class could multiply  142857 by 6  so the majority were not impressed when I  revealed the answer as  857 142 ,

Later in the day we took out calculators  and looked at turning fractions into decimal numbers

1/2   = 0.5

1/3 = 0.333

1/4 = 0.25

1/7 =

2/7 =

3/7 =

etc.

We discussed the pattern that we saw in the decimal answers for the sevenths.

 

Web Sites

Wikipedia on 142857

 

 leave a comment on the Math Wall

 

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Last updated: 01/02/13.