# Task 10.2

In the decimal representation of the number ${ }^{1 / 7}$, the 2021st digit after the decimal point was crossed out (and the other digits were not changed). Did the number increase or decrease?

## Number of points 7

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# Answer:

increased

## Solution

By dividing the numerator by the denominator, we get that $1 / 7 = 0.(142857)$.

This means that the period of the resulting fraction contains 6 digits.

Since the number 2021, when divided by 6, gives a remainder of 5, the 2021st digit after the decimal point in the decimal representation of the number $1 / 7$ is the fifth digit of the period, which is the digit 5.

After erasing it, the digit in this position will be 7.

Therefore, the original number has increased.

## Additional Criteria

Identified only the period of the fraction - 3 points

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