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What is the tenth digit of the decimal expansion of 1234/9999 after the decimal point?a.4b.3c.2d.1

What is the tenth digit of the decimal expansion of 1234/9999 after the decimal point-example-1
User Hasintha Janka
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We have to find the tenth digit of the decimal expansion of 1234/9999 after the decimal point.

We estimate that this will be a periodic number. We then can find its decimal expression as:


x=0.12341234123412341234\ldots

NOTE: when the denominator is a number with all digits equal to 9, the resulting decimal is a periodic decimal with the numerator repeating with a number of digits equal to the number of digits of the denominator.

In this case, we have 9999, so we have 4 digits. Then, the decimal will repeat "1234", a four digit number. If the numerator has more digits, then we would have a mixed number and the whole part should be treated separately.

Then, now we can count. We have 8 decimal digits for the first two repetitions and then 1 for the 9th place and 2 for the 10th place.

Then, the tenth digit of the decimal expansion is 2.

Answer: 2 [Option C]

User Leantraxxx
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