only repeating decimals can be converted to a rational number.
A is the only choice here.
Suppose it has a value, say, x. Then
10000x = 8743.87438743...
x = 0.87438743...
If you subtract, then that gives you
9999x = 8743.0000000...
x = 8743/9999
Or, if you have studied geometric series, you can see that
a = 0.8743
r = 0.00001
and the infinite sum is .8743/.9999
In general, the repeating digits can be placed over that many 9's to form a rational number. Of course, leading zeroes can complicate things.
0.232323 = 23/99
0.00232323 = 23/9900
and so on
**URGENT** Which of these nonterminating decimals can be converted into a rational number?
a. 0.874387438743..
b. 0.0000100020003..
c. 5.891420975..
d. 10.07401295..**
am i correct? if not please explain how to do it correctly because i'm struggling and this is due in an hour.
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