To convert 4/15 to a decimal using long division, follow these steps:
1. Write 4 as the dividend and 15 as the divisor.
2. Perform long division by dividing the first digit of the dividend (4) by the divisor (15). The quotient is 0.
3. Write 0 above the line and multiply it by the divisor:
0 * 15 = 0
4. Subtract the result (0) from the first digit of the dividend (4):
4 - 0 = 4
5. Bring down the next digit of the dividend (0) and write it next to the remainder:
4
6. Now, divide 40 (the new dividend) by 15 (the divisor). The quotient is 2.
40 ÷ 15 = 2
7. Write 2 above the line and multiply it by the divisor:
2 * 15 = 30
8. Subtract the result (30) from the new dividend (40):
40 - 30 = 10
9. Bring down the next digit of the dividend (0) and write it next to the remainder:
10
10. Divide 100 (the new dividend) by 15 (the divisor). The quotient is 6.
100 ÷ 15 = 6
11. Write 6 above the line and multiply it by the divisor:
6 * 15 = 90
12. Subtract the result (90) from the new dividend (100):
100 - 90 = 10
13. Bring down the next digit of the dividend (0) and write it next to the remainder:
10
14. Divide 100 (the new dividend) by 15 (the divisor) again. The quotient is 6.
100 ÷ 15 = 6
15. Write 6 above the line and multiply it by the divisor:
6 * 15 = 90
16. Subtract the result (90) from the new dividend (100):
100 - 90 = 10
17. The remainder is 10, and it repeats in a pattern. Since we know the remainder will continue, we can add a decimal point and continue the long division process indefinitely:
0.266666...
Therefore, 4/15 as a decimal is approximately 0.2666... (repeating).