How do you evaluate 114\div 268114÷268?
1 Answer
Explanation:
To get a completely accurate answer, long divide until the remainder repeats.
With a long division of this kind, it is often helpful to write down the single digit multiples of the divisor first:
1: color(white)(0)2681:0268
2: color(white)(0)5362:0536
3: color(white)(0)8043:0804
4: 10724:1072
5: 13405:1340
6: 16086:1608
7: 18767:1876
8: 21448:2144
9: 24129:2412
Then we find:
In this example, note that the remainder
So we find:
114/268 = 0.4bar(253731343283582089552238805970149)114268=0.4¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯253731343283582089552238805970149
where the bar indicates the sequence of digits which repeat.
Any division of two whole numbers will eventually repeat since the running remainder is always smaller than the divisor. So any rational number is representable as a decimal expansion which eventually repeats or terminates (i.e. repeats