in the number 0.123451234512345.........(recurring)what is the 1992th digit after the decimal point?
goes in pattern 12345
find the remainder when divided by 5.
It is 2.
Thus it is 2. (coincidentally)
1992/5=376 groups of five, so the last digit is a 5.
Wait...isnt 1992 not divisible by 5...? It has a remainder of 2 so it would be 2 right?
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
To find the 1992nd digit after the decimal point in the recurring decimal 0.123451234512345..., we can follow these steps:
Step 1: Determine the pattern
Observe the recurring pattern in the decimal: 12345. The pattern repeats after every five digits.
Step 2: Find the number of complete patterns
To find the number of complete patterns up to the 1992nd digit, divide 1992 by 5: 1992 ÷ 5 = 398 remainder 2.
Step 3: Find the position within the pattern
Since there are 398 complete patterns, we need to find the 2nd digit in the pattern (remainder 2). The second digit in the pattern is 2.
Step 4: Identify the digit
The 1992nd digit after the decimal point is 2.
Therefore, the 1992nd digit after the decimal point in the recurring decimal 0.123451234512345... is 2.