When does the fraction \(\displaystyle{\frac{{{142}}}{{{2.54}}}}\) ever repeat?

Kinley Padilla

Kinley Padilla

Answered question

2022-03-13

When does the fraction 1422.54 ever repeat?

Answer & Explanation

Quiensesoipsyc8n

Quiensesoipsyc8n

Beginner2022-03-14Added 3 answers

Step 1
Note that
1422.54=100×71127
Since 127 is ', it may well happen that the decimal expansion of 71127 is periodic with period 126. But that's not the case. It turns out that it is periodic with period
42(=1263)
71127=0.559,055,118,110,236,220,472,440,944,881,889,763,779,52742  digits
and then it repeats itself over and over.

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