Answer :
To express the fraction [tex]\(\frac{13}{15}\)[/tex] in decimal form, you need to divide 13 by 15.
1. Set Up the Division: Start by dividing the numerator (13) by the denominator (15).
2. Perform the Division:
- 15 goes into 13 zero times, so you place a 0 before the decimal point.
- Consider 130 (by adding a decimal point and a zero to 13).
- 15 goes into 130 eight times (because [tex]\(15 \times 8 = 120\)[/tex]).
- Subtract 120 from 130 to get a remainder of 10.
3. Continue the Division:
- Bring down a 0, making it 100.
- 15 goes into 100 six times (because [tex]\(15 \times 6 = 90\)[/tex]).
- Subtract 90 from 100 to get a remainder of 10.
4. Repeat the Process:
- Again, bring down another 0 (making it 100 once more).
- 15 goes into 100 six times, just like before, continuing with the remainder of 10.
5. Recognizing the Pattern:
- The process continues similarly, repeatedly obtaining a remainder of 10, so you see the digits start to repeat.
Thus, the decimal representation of [tex]\(\frac{13}{15}\)[/tex] is a repeating decimal: [tex]\(0.8666\ldots\)[/tex], which can also be written as [tex]\(0.86\overline{6}\)[/tex] to indicate the repeating 6.
1. Set Up the Division: Start by dividing the numerator (13) by the denominator (15).
2. Perform the Division:
- 15 goes into 13 zero times, so you place a 0 before the decimal point.
- Consider 130 (by adding a decimal point and a zero to 13).
- 15 goes into 130 eight times (because [tex]\(15 \times 8 = 120\)[/tex]).
- Subtract 120 from 130 to get a remainder of 10.
3. Continue the Division:
- Bring down a 0, making it 100.
- 15 goes into 100 six times (because [tex]\(15 \times 6 = 90\)[/tex]).
- Subtract 90 from 100 to get a remainder of 10.
4. Repeat the Process:
- Again, bring down another 0 (making it 100 once more).
- 15 goes into 100 six times, just like before, continuing with the remainder of 10.
5. Recognizing the Pattern:
- The process continues similarly, repeatedly obtaining a remainder of 10, so you see the digits start to repeat.
Thus, the decimal representation of [tex]\(\frac{13}{15}\)[/tex] is a repeating decimal: [tex]\(0.8666\ldots\)[/tex], which can also be written as [tex]\(0.86\overline{6}\)[/tex] to indicate the repeating 6.
