Units of measurement: base 60

In base 60, every number is represented a a combination of powers of 60. Thus, introducing ; as a sexagesimal point, we get

67 = 1.60 + 7, so 1, 7

136 = 2.60 + 16, so 2, 16
1/2 = 30/60, so 0 ; 30
  3/5 = 36/60, so 0 ; 36  etc.

Now try these:

In base 60,     

             1.
981 = 21, 16   ;
     16, 21  ;
neither of these  .
             2.
981/3600 = 0 ; 21, 16  ;

0 ; 16, 21  ;

neither of these  .

And for a harder challenge, can you explain why

              3.         60/59 = 1; 1, 1, 1, ... ?                                                  

The Babylonians would definitely not have liked this problem!  

The right hand side expands as

1 + 1/60 + 1/602 + 1/603 + ...

= 1 / (1 – 1/60) (summing the geometric series)

= 60/59 as required.                                           


This answer is incorrect.

Did you try dividing 981 by 60?


This answer is incorrect.

Did you try expanding 981 as a
linear combination of powers of 60?