Answer :
Answer:
Step-by-step explanation:
To convert the fraction \( \frac{4}{13} \) to its decimal expansion, we perform the division of 4 by 13.
Let's divide 4 by 13 using long division:
1. 4 divided by 13 is 0. Since 4 is less than 13, we put a 0 before the decimal point.
2. Append a decimal point and a zero to 4, making it 40. Now divide 40 by 13.
- 13 goes into 40 three times (3 * 13 = 39), so the first digit after the decimal is 3.
- Subtract 39 from 40 to get a remainder of 1.
3. Append another zero to the remainder, making it 10. Now divide 10 by 13.
- 13 goes into 10 zero times, so the next digit is 0.
- The remainder remains 10.
4. Append another zero to the remainder, making it 100. Now divide 100 by 13.
- 13 goes into 100 seven times (7 * 13 = 91), so the next digit is 7.
- Subtract 91 from 100 to get a remainder of 9.
5. Append another zero to the remainder, making it 90. Now divide 90 by 13.
- 13 goes into 90 six times (6 * 13 = 78), so the next digit is 6.
- Subtract 78 from 90 to get a remainder of 12.
6. Append another zero to the remainder, making it 120. Now divide 120 by 13.
- 13 goes into 120 nine times (9 * 13 = 117), so the next digit is 9.
- Subtract 117 from 120 to get a remainder of 3.
7. Append another zero to the remainder, making it 30. Now divide 30 by 13.
- 13 goes into 30 two times (2 * 13 = 26), so the next digit is 2.
- Subtract 26 from 30 to get a remainder of 4.
Since the remainder is back to 4, which was our initial number, the digits will start repeating from here.
So, the decimal expansion of \(\frac{4}{13}\) is:
\[ 0.\overline{307692} \]
This means that the decimal expansion of \(\frac{4}{13}\) is \( 0.307692307692\ldots \), where the sequence "307692" repeats indefinitely.
Answer:
0.3077
Step-by-step explanation:
4/13 = 0.30769
after round off, 0.3077