To convert the fraction [tex]\(\frac{9}{41}\)[/tex] into a decimal, you need to perform the division of the numerator (9) by the denominator (41). Here's a detailed, step-by-step solution for this process:
1. Set up the division: You need to divide 9 by 41.
2. Perform the division: When you divide 9 by 41 using long division:
- 41 goes into 90 (the first two digits of 900) exactly 2 times (since [tex]\(41 \times 2 = 82\)[/tex]).
- Subtract 82 from 90 to get a remainder of 8.
- Bring down the next 0 to make it 80. Now, 41 goes into 80 only 1 time (since [tex]\(41 \times 1 = 41\)[/tex]).
- Subtract 41 from 80 to get a remainder of 39.
- Bring down the next 0, making it 390. 41 goes into 390 exactly 9 times (since [tex]\(41 \times 9 = 369\)[/tex]).
- Subtract 369 from 390 to get a remainder of 21.
- Bring down another 0 to make it 210. 41 fits into 210 5 times (since [tex]\(41 \times 5 = 205\)[/tex]).
- Subtract 205 from 210 to get a remainder of 5.
- Continue this process to get further decimal places, if desired.
3. Combine the results: The process will yield the result as 0.21951219512195122, which can be rounded according to your preferred precision.
Thus, [tex]\(\frac{9}{41}\)[/tex] expressed as a decimal is [tex]\(0.21951219512195122\)[/tex]. When rounded to five decimal places, it is [tex]\(0.21951\)[/tex].
