it can be converted into fraction
1) real number
2) Irrational numbers
3) Rational number
4) None
Answers
Answer:
Rational Number
Step-by-step explanation:
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Answer:
Well, the question is a little off, because a rational number is, by definition, a fraction (i.e. the ratio of two integers). No “conversion” is needed.
I assume you’re thinking of a rational number expressed in decimal form, which may be never-ending. But every rational number in decimal form must, at some point, have a repeating sequence of digits.
A simple example is 1/3 = 0.3333333…, or 0.3¯¯¯.
A longer repeating sequence is 2/7 = 0.285714284714… or 0.285714¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯.
If you start with the decimal expansion of a rational number, you can express it in fractional form by finding (1) the integer part, (2) the non-repeating part, and (3) the repeating part. For example, suppose you have:
2.318181818… = 2.318¯¯¯¯¯
Then the integer part is 2, the non-repeating part is 3 and the repeating part is 18. You just express each part as a fraction and sum them together.
The non-repeating part is simply divided by 10n where n is the number of non-repeating digits. In this case n=1, so we have 3/10.
The repeating part is divided by (10n+k)−1 , where k is the length of the repeating digits. In this case n=1 and k=2, so we have 18/999.
Summing together, we have:
2 + (3/10) + (18/999), which simplifies to 2 + 353/1110.
Step-by-step explanation:
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