Maths questions on recurring decimals?

2013-10-01 7:35 pm
Prove that 1.03 recurring = 34/33
Prove that 0.07 recurring = 7/99
Prove that 0.539 recurring = 539/999

回答 (1)

2013-10-01 7:40 pm
✔ 最佳答案
1.030303 ? is that what you mean? You have to tell us which digits repeat?
or is it 1.03103103?

I'll assume the first.
let x = 0.0303030 ...
100x = 3.0303030
100x – x = 3.030303.. – 0.030303 ... = 3
100x – x = 3
99x = 3
x = 3/99 = 1/33
add 1
1.030303... = 1 + (1/33) = 34/33

0.070707
let x = 0.070707...
100x = 7.070707
100x – x = 7
99x = 7
x = 9/99

0.539539 ...
x = 0.539539 ...
1000x = 539.539539 ...
1000x – x = 539
x = 539/999


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