Find the 100th place to the right of the decimal point in the decimal expansion of 1/13.
1/13 = 0.076923 076923 ...
You can see here that the repeating numbers are 076923. There are six numbers in all so,
100/6 = 16 remainder 4
Counting four places, the 100th place is 9.
Thanks, that makes sense!
Well, well, well! Let's have some decimal fun, shall we? Now, since we're dealing with the fraction 1/13, we need to find the decimal expansion.
To do that, we'll divide 1 by 13. So, let me grab my clown calculator and...ta-da! The decimal expansion of 1/13 is approximately 0.07692307692307... and it goes on and on.
Now, you wanted to find the 100th place after the decimal point, huh? That's quite a task! But we'll tackle it together.
If we take a closer look at the repeating part of the decimal 0.07692307692307..., we'll see that it repeats every 6 digits. So, let's find where our 100th digit falls in that repeating pattern.
Dividing 100 by 6 gives us a remainder of 4. So, that means our 100th digit will be the same as the 4th digit in the repeating pattern.
Now, let's count! Starting from the decimal point, the 4th digit in the repeating pattern is...*drumroll*...2!
Therefore, the 100th digit to the right of the decimal point in the decimal expansion of 1/13 is 2.
I hope I was clown-tastically helpful!
To find the 100th place to the right of the decimal point in the decimal expansion of 1/13, we need to divide 1 by 13.
1 ÷ 13 = 0.0769230769...
The decimal expansion of 1/13 is a recurring decimal, meaning it repeats the group of digits "076923" indefinitely.
Since the question asks for the 100th place to the right of the decimal point, we can see that the repeating group of 6 digits will be repeated in blocks of 2. Therefore, the 100th place to the right of the decimal point is the same as the 2nd place in the repeating group.
So, the 100th place to the right of the decimal point in the decimal expansion of 1/13 is "7".
To find the 100th place to the right of the decimal point in the decimal expansion of 1/13, we can perform long division. Here's how:
1. Begin by writing down the fraction as a division problem: 1 ÷ 13.
2. Perform long division by dividing 1 by 13.
3. The quotient will be 0 followed by a decimal point since 1 is less than 13. Write a 0 and a decimal point and bring down a 0 after the decimal.
4. Divide 10 by 13. The quotient will be 0, and the remainder will be 10.
5. Multiply the remainder 10 by 10 to get 100. Then divide 100 by 13. The quotient will be 7, and the remainder will be 9.
6. Continue this process until you have reached the desired decimal place or until the division terminates.
After several iterations, you will find that the remainder pattern repeats. In this case, the decimal expansion of 1/13 is 0.0769230769…
Since the remainder pattern repeats after every 6 digits (0.076923), we can determine that the 100th place to the right of the decimal point will be the same as the 4th place (6) in the remainder pattern.
Therefore, the 100th place to the right of the decimal point in the decimal expansion of 1/13 is 6.