To convert the fraction [tex]\(\frac{47}{4}\)[/tex] into a decimal, follow these steps:
1. Identify the numerator and the denominator:
- The numerator is 47.
- The denominator is 4.
2. Set up the division:
- You need to divide 47 by 4.
3. Perform the division:
- Determine how many times 4 can go into 47 without exceeding it.
- 4 goes into 47 a total of 11 times because [tex]\(4 \times 11 = 44\)[/tex].
- There will be a remainder of [tex]\(47 - 44 = 3\)[/tex].
4. Handle the remainder:
- To continue dividing, you bring down a 0, making the remainder 30.
- Determine how many times 4 can go into 30.
- 4 goes into 30 a total of 7 times because [tex]\(4 \times 7 = 28\)[/tex].
- There will be a new remainder of [tex]\(30 - 28 = 2\)[/tex].
5. Continue the division process:
- Bring down another 0, making the remainder 20.
- Determine how many times 4 can go into 20.
- 4 goes into 20 a total of 5 times because [tex]\(4 \times 5 = 20\)[/tex].
- There will be no more remainder as [tex]\(20 - 20 = 0\)[/tex].
6. Combine the results:
- The whole number part is 11.
- The fractions parts are 0.7 and 0.05.
Therefore, combining all parts together, the decimal representation of the fraction [tex]\(\frac{47}{4}\)[/tex] is [tex]\(11.75\)[/tex].
