For number nerds (more power to us!): The decimal expansion of 1/7 has a remarkable property. It is .142857 repeated. Notice that 14 = 2x7, 28 = 2x14, 56 = 2x28, and 2x56 = 112 which gives the next digit in 1428571... and the hundreds digit adds to 56 to make the 57 at the end of the 6-digit repeating sequence. In fact, here is 1/7 as the sum of multiplying 7 by 2/100 many times, and adding:
.14
.0028
.000056
.00000112
.0000000224
etc.
Yes, it adds up to the repeating decimal. The only other number that gives such a property is 1/3 = .333333...:
.3
.03
.003
and keep multiplying by 3/10 and adding.
This was an open problem in mathematics for years until solved by a student, Kevin Ford, in the American Mathematical Monthly of February, 1993, page 192.
For number nerds (more power to us!): The decimal expansion of 1/7 has a remarkable property. It is .142857 repeated. Notice that 14 = 2x7, 28 = 2x14, 56 = 2x28, and 2x56 = 112 which gives the next digit in 1428571... and the hundreds digit adds to 56 to make the 57 at the end of the 6-digit repeating sequence. In fact, here is 1/7 as the sum of multiplying 7 by 2/100 many times, and adding:
.14
.0028
.000056
.00000112
.0000000224
etc.
Yes, it adds up to the repeating decimal. The only other number that gives such a property is 1/3 = .333333...:
.3
.03
.003
and keep multiplying by 3/10 and adding.
This was an open problem in mathematics for years until solved by a student, Kevin Ford, in the American Mathematical Monthly of February, 1993, page 192.