How many digits are in the repeating cycle of 17/27?
1. 3
2. 5/12
3. 0.538461 with a line over the .538461
4.8/9
5.100
The correct answer is 3.
To find the repeating cycle of a fraction, we can convert the fraction to its decimal representation.
When we divide 17 by 27, we get 0.629629629..., and the repeating cycle is 629.
Therefore, the fraction 17/27 has a repeating cycle of 3 digits.
To find the repeating cycle of a fraction, you can use long division.
Let's calculate the repeating cycle of 17/27 step-by-step:
1. Start by dividing 17 by 27:
- The quotient is 0, and the remainder is 17.
2. Multiply the remainder (17) by 10 and divide it by the denominator (27):
- 17 * 10 = 170
- 170 / 27 = 6 remainder 8
3. Repeat step 2 with the new remainder (8):
- 8 * 10 = 80
- 80 / 27 = 2 remainder 26
4. Repeat step 2 again with the new remainder (26):
- 26 * 10 = 260
- 260 / 27 = 9 remainder 17
5. The remainder 17 repeats, starting the cycle again.
Therefore, the repeating cycle of 17/27 is 0.6296296296... The cycle consists of 6 digits, which are 629629.
So, the correct answer would be:
The repeating cycle of 17/27 is 5.