sevenths as a decimal

the repeating pattern for sevenths written as a decimal is fairly easily remembered since it goes            14 28 57 which is
double 7,
double 14,
double 28 ... oops!

the reasons for this are:

• 100 divided by 7 is 14 remainder 2
• so the next block of two digits will be the result of dividing 200 by 7, which is 28 (remainder 4)
• so the next block of two digits will be the result of dividing 400 by 7, which is 57 (not 56) remainder 1; after which the process repeats itself

if you split the six digit (printing) block for sevenths into two parts and add them: 142 + 857 you get 999 and if you split it into three parts and add them: 14 + 28 + 57 you get 99

this neat property is shared by the block of six repeating numbers for thirteenths and other decimal equivalents to fractions

and also, it might be interesting to note that ...