Dividing by 7, Fast!

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Abstract

2/7 = 0.285714 (repeating)3/7 = 0.428571 (repeating)4/7 = 0.571428 (repeating)5/7 = 0.714285 (repeating)6/7 = 0.857142 (repeating)So if you remember the sequence 142857, and can figure out what the first digit of the decimal is, you can determine what the remaining five digits of the repeating sequence will be, as they’ll a # Options lways follow that sequence.How do we use this in practice?Say you have 107/7. This is 100/7 + 7/7, so 100/7 + 1.Then 100/7 is 1/7 * 100, and we know 1/7 is going to be 0.142857 (repeating). Multiplying by 100 means we move the decimal places two spots to the right, so we get 14.285714 (repeating), and then we add one, so we get 15.285714 (repeating).</article></body>

This is a fun math trick!

1/7 is 0.142857 (repeating). Those six digits are very interesting, as we’ll see:

2/7 = 0.285714 (repeating)

3/7 = 0.428571 (repeating)

4/7 = 0.571428 (repeating)

5/7 = 0.714285 (repeating)

6/7 = 0.857142 (repeating)

So if you remember the sequence 142857, and can figure out what the first digit of the decimal is, you can determine what the remaining five digits of the repeating sequence will be, as they’ll always follow that sequence.

How do we use this in practice?

Say you have 107/7. This is 100/7 + 7/7, so 100/7 + 1.

Then 100/7 is 1/7 * 100, and we know 1/7 is going to be 0.142857 (repeating). Multiplying by 100 means we move the decimal places two spots to the right, so we get 14.285714 (repeating), and then we add one, so we get 15.285714 (repeating).