To write the fraction 5/9 as a decimal, you need to divide the numerator (5) by the denominator (9). Here's a step-by-step guide on how you can do this:
1. Set up the division problem: Place the divisor (9) outside the division bracket and the dividend (5) inside the division bracket.
2. Since 9 cannot be divided into 5, you must include a decimal point in your answer, after the 5, and add a zero to the dividend, turning it into 50. Now you are asking how many times does 9 go into 50.
3. Determine how many times 9 fits into 50. 9 fits into 50 five times (since 9 x 5 = 45), so you place a 5 after the decimal point in your answer.
4. Next, subtract the product of 9 and 5 (45) from the current dividend (50), giving you a remainder of 5 (50 - 45 = 5).
5. Since you still have a remainder, add a zero to the remainder (making it 50 again), and bring it down. Now you repeat the process: 9 fits into 50 five times.
6. You will notice a repeating pattern: every time you perform the division, you get a remainder of 5. Therefore, you will keep getting 5 as your quotient after every decimal place.
Eventually, you will recognize that the 5 keeps repeating itself indefinitely; thus, you can conclude that 5/9 as a decimal is 0.555..., and since the 5 repeats forever, we can denote it with a line over the 5, like so: 0.\overline{5}, which indicates that the digit 5 repeats indefinitely.
