What is the 43rd digit after the decimal point in the decimal representation of 1/13?
actually i just checked and it said it was 7
1/13 = 0.0769230769230...
The repeating numbers are 076923 (six numbers), thus,
43 / 6 = 7 remainder 1.
Therefore counting from zero, the 43rd digit after the decimal point is 0.
hope this helps. :3
omg she is right
Well, you've certainly caught me by surprise with your mathematical curiosity! Let me juggle the numbers for a moment...
Ah, the 43rd digit after the decimal point in the decimal representation of 1/13 is... drumroll please... 6! Yes, it's quite a little rascal hiding in there. Just remember, finding that sneaky 43rd digit is like uncovering the final piece of a clown puzzle. Happy number hunting!
To find the 43rd digit after the decimal point in the decimal representation of 1/13, we can use long division.
Step 1: Divide the numerator (1) by the denominator (13) using long division. We start with 0 as the quotient.
0.
Step 2: Multiply the quotient (0) by the denominator (13) and subtract it from the numerator (1).
1 - 0 × 13 = 1.
Step 3: Bring down a zero and update the numerator with the new value.
10.
Step 4: Now, divide the new numerator (10) by the denominator (13). Add the result to the quotient obtained so far.
0.0.
Step 5: Multiply the new quotient (0) by the denominator (13) and subtract it from the new numerator (10).
10 - 0 × 13 = 10.
Step 6: Bring down a zero and update the numerator.
100.
Step 7: Repeat the above steps until we either obtain a remainder of zero or have obtained enough decimal places to determine the 43rd digit.
Continuing the process:
1st division: 10 ÷ 13 = 0.769230769...
2nd division: 90 ÷ 13 = 6.923076923...
3rd division: 40 ÷ 13 = 3.076923076...
4th division: 70 ÷ 13 = 5.384615384...
5th division: 50 ÷ 13 = 3.846153846...
6th division: 40 ÷ 13 = 3.076923076...
7th division: 70 ÷ 13 = 5.384615384...
As we can see, the remainder starts repeating after a certain point. This indicates that the decimal representation of 1/13 is a repeating decimal.
To find the 43rd digit after the decimal point, we need to find the repeating pattern.
In this case, the repeating pattern begins after the 2nd division with the digit 6.923076923... repeating indefinitely. The pattern is a block of 6 digits: 923076.
Since 43 divided by 6 equals 7 remainder 1, it means that the 43rd digit after the decimal point is the 1st digit in the repeating pattern, which is 9.
Therefore, the 43rd digit after the decimal point in the decimal representation of 1/13 is 9.