# math

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in the number 0.123451234512345.........(recurring)what is the 1992th digit after the decimal point?

• math -

goes in pattern 12345

find the remainder when divided by 5.

It is 2.

Thus it is 2. (coincidentally)

• math -

1992/5=376 groups of five, so the last digit is a 5.

• math -

Wait...isnt 1992 not divisible by 5...? It has a remainder of 2 so it would be 2 right?

• math -

1992 ÷ 5 leaves a remainder of 2 (then length of the period is 5, that's why I divided by 5)

Look at the 7th digit after the decimal place
when I divide 7 by 5 I get a remainder of 2
when I divide 12 by 5 I get a remainder of 2
when I divide 17 by 5 I get a remainder of 2

the 7th digit, the 12th digit and the 17th digit are each equal to 2
so the 1992nd digit is a 2

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