To convert the fraction \( \frac{4}{15} \) into a decimal using long division, we perform the following steps:
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Set up the division: We want to divide 4 by 15. Since 4 is less than 15, we recognize that the integer part of the result is 0. We will begin with 4.000000 to perform the division.
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Perform the long division:
- 15 goes into 40 two times (since \( 15 \times 2 = 30 \)).
- Subtract 30 from 40, which gives us 10.
- Bring down the next digit (which is 0) making it 100.
- Now, determine how many times 15 goes into 100. It goes six times (since \( 15 \times 6 = 90 \)).
- Subtract 90 from 100, which gives us 10 again.
- Bring down the next 0, making it 100 again.
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Repeat the process:
- Again, determine how many times 15 goes into 100. It goes six times, giving \( 15 \times 6 = 90 \).
- Subtract 90 from 100, which gives us 10.
- Bring down the next 0, and we are back to the same situation.
This process will keep repeating indefinitely, resulting in \( 0.26666\ldots \).
- Conclusion: The decimal representation of \( \frac{4}{15} \) is \( 0.\overline{26} \), meaning that the digits "26" repeat indefinitely.
Thus, \( \frac{4}{15} \) as a decimal is \( 0.266666\ldots \) or \( 0.26\overline{6} \).