Question

What is the 358th digit after the decimal point in the repeating decimal .3178

Answer 1

Answer: 1

If the 3178 block repeats forever, then we need to divide by 4 to look at the remainder. This is simply because the block is 4 values wide.

358/4 = 89 remainder 2

The remainder 2 means we're on the 2nd slot of "3178", so we circle the "1" as the final answer.

The 358th digit after the decimal point in 0.31783178... is 1.

If you aren't convinced, then try a smaller value instead of 358. Let's say we picked the 7th digit

7/4 = 1 remainder 3

The remainder 3 means we look at the 3rd slot of 3178. The 7th digit is 7.

Another example: The 10th digit is 1 because 10/4 = 2 remainder 2. The 1 is in the 2nd slot of 3178, so it's also in the 10th slot.

Side note: If you get remainder 0, then treat it as remainder 4. Both mean the same thing when dividing by 4.

Answer 2

The 358th digit after the decimal point in the repeating decimal 0.3178 is '1', determined by taking the remainder of 358 divided by the length of the repeating sequence.

Step-by-step explanation:

The question asks about the 358th digit after the decimal point in the repeating decimal 0.3178. This decimal repeats the digits 3178 indefinitely. Since it's a repeating sequence of 4 digits, we can find out which digit will be in the 358th position after the decimal by calculating the remainder when 358 is divided by 4 (the length of the repeating sequence).

358 divided by 4 equals 89 with a remainder of 2. This means that after 89 complete cycles of '3178,' the next digit (the 1st of the next cycle) would be '3' and the second (which is our 358th digit) would be '1'. So, the 358th digit after the decimal point in the repeating decimal 0.3178 is '1'.