To convert the fraction [tex]\(\frac{6}{13}\)[/tex] to a decimal, we will use long division:
1. Setup the division:
- 6 is the numerator (dividend).
- 13 is the denominator (divisor).
2. Division step-by-step:
- 13 does not go into 6, so we place a 0 before the decimal point.
- We add a decimal point and some zeros to the right of the 6 to continue the division process: [tex]\(6.000000...\)[/tex].
3. Convert 6 to 60:
- 13 goes into 60 four times because [tex]\(13 \times 4 = 52\)[/tex].
- Write 4 in the quotient place: 0.4.
- Subtract 52 from 60, which gives us a remainder of 8.
4. Bring down 0 making it 80:
- 13 goes into 80 six times because [tex]\(13 \times 6 = 78\)[/tex].
- Write 6 in the quotient, so we have 0.46.
- Subtract 78 from 80, which gives us a remainder of 2.
5. Bring down another 0 making it 20:
- 13 goes into 20 one time because [tex]\(13 \times 1 = 13\)[/tex].
- Write 1 in the quotient, so we have 0.461.
- Subtract 13 from 20, leaving a remainder of 7.
6. Bring down another 0 making it 70:
- 13 goes into 70 five times because [tex]\(13 \times 5 = 65\)[/tex].
- Write 5 in the quotient, so we have 0.4615.
- Subtract 65 from 70, leaving a remainder of 5.
7. Bring down another 0 making it 50:
- 13 goes into 50 three times because [tex]\(13 \times 3 = 39\)[/tex].
- Write 3 in the quotient, so we have 0.46153.
- Subtract 39 from 50, leaving a remainder of 11.
8. Bring down another 0 making it 110:
- 13 goes into 110 eight times because [tex]\(13 \times 8 = 104\)[/tex].
- Write 8 in the quotient, so we have 0.461538.
- Subtract 104 from 110, leaving a remainder of 6.
At this point, we notice that we are repeating the initial division with 6, so this will be a repeating decimal.
Using these steps, dividing [tex]\(6\)[/tex] by [tex]\(13\)[/tex] using long division results in a decimal approximation of:
[tex]\[ 0.46153846153846156 \][/tex]
So, [tex]\(\frac{6}{13} \approx 0.46153846153846156\)[/tex] (with repeating nature).
