Answer :
To convert the fraction [tex]\(\frac{14}{15}\)[/tex] into a decimal using long division, you can follow these steps:
1. Set up the division problem so that 14 is divided by 15. Here, 14 is the dividend, and 15 is the divisor.
2. Since 14 is less than 15, it cannot be divided by 15 without going into fractions, so we'll consider decimal values. Begin by placing a decimal point in the quotient and adding a zero to the dividend, making it 140.
3. Divide 140 by 15. The result is 9 because 15 times 9 is 135.
4. Subtract 135 from 140, which leaves a remainder of 5.
5. Bring down another 0, making it 50.
6. Divide 50 by 15, which gives 3 because 15 times 3 is 45.
7. Subtract 45 from 50, leaving a remainder of 5 again.
8. Continue this process. Each time bringing down a 0 and dividing. You will notice that the remainder of 5 will keep repeating, leading to a repeating decimal sequence.
9. The resulting decimal is [tex]\(0.9333...\)[/tex] with the digit 3 repeating indefinitely.
Thus, the decimal representation of [tex]\(\frac{14}{15}\)[/tex] is approximately 0.9333, a repeating decimal.
1. Set up the division problem so that 14 is divided by 15. Here, 14 is the dividend, and 15 is the divisor.
2. Since 14 is less than 15, it cannot be divided by 15 without going into fractions, so we'll consider decimal values. Begin by placing a decimal point in the quotient and adding a zero to the dividend, making it 140.
3. Divide 140 by 15. The result is 9 because 15 times 9 is 135.
4. Subtract 135 from 140, which leaves a remainder of 5.
5. Bring down another 0, making it 50.
6. Divide 50 by 15, which gives 3 because 15 times 3 is 45.
7. Subtract 45 from 50, leaving a remainder of 5 again.
8. Continue this process. Each time bringing down a 0 and dividing. You will notice that the remainder of 5 will keep repeating, leading to a repeating decimal sequence.
9. The resulting decimal is [tex]\(0.9333...\)[/tex] with the digit 3 repeating indefinitely.
Thus, the decimal representation of [tex]\(\frac{14}{15}\)[/tex] is approximately 0.9333, a repeating decimal.
