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hoa [83]
3 years ago
10

erika says that no matter how many decimals places she divides to when she divides 1 by 3, the digit 3 in the quotient will just

keep repeating. Is she correct? explain.
Mathematics
2 answers:
torisob [31]3 years ago
6 0

Answer:

Yes, Erica is correct.

We divide 1 by 3 as \frac{1}{3} =0.333333...

Now, the quotient is 0.333333...

Clearly, we can see that the 3 is repeating.

Now, the decimal expansion of any rational number is non-terminating repeating if the factors of the denominator is not of the form

2^{m} \times5^{n} .

Clearly, the factor of the denominator, i.e 3 is 3\times1

So, the factors are not of the form 2^{m} \times5^{n} , the decimal expansion of \frac{1}{3} is non-terminating repeating.

Hence, the digit 3 in the quotient is repeating.

lara [203]3 years ago
4 0
Yes she is correct because 1 divided by 3 will have an infinite number of 3s
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