how many digits are in repeating cycle of 17 over 27?
To figure out the repeating cycle of the decimal representation of 17/27, we need to perform the long division:
0.629629629...
When we continue the long division, we see that the decimal 629 repeats indefinitely. Thus, the repeating cycle contains 3 digits, which are 629.
it says its wrong
Apologies for the mistake. Let me try again.
To find the repeating cycle of 17/27, we perform the long division:
0.629629629...
The repeating cycle in this case is 629, which consists of 3 digits.
629 is not the right answer
Apologies for the confusion. Let's try again.
To find the repeating cycle of 17/27, we can perform long division:
0.629629...
In this case, the repeating cycle is 629, which consists of 3 digits.
wait im dumb you were right the whole time my bad i apologize
No problem at all! It happens to everyone. If you have any more questions, feel free to ask.
which of the following rational numbers can be expressed as a repeating decimal: 7 over 8, 5 over 12, 17 over 25, or 31 over 40?
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to find their decimal representations.
1) 7/8 = 0.875
2) 5/12 = 0.416666...
3) 17/25 = 0.68
4) 31/40 = 0.775
Out of the given options, only 5/12 (0.416666...) can be expressed as a repeating decimal since the decimal part repeats indefinitely.
To find the number of digits in the repeating cycle of the fraction 17/27, you need to perform long division. Here's how you can do it:
1. Start by dividing 17 by 27. The quotient will be your integer part (if any) and the remainder will be the dividend for the next step.
- Dividing 17 by 27 gives you 0 as the quotient and 17 as the remainder.
2. Multiply the remainder (17) by 10, and then divide by the divisor (27). This will give you the next digit in the decimal expansion.
- (17 * 10) / 27 = 6 (approximately)
3. Repeat step 2 until you either find a repeating pattern or all the decimals terminate.
- Multiply the remainder (17) by 10: 17 * 10 = 170. Divide it by the divisor (27): 170 / 27 = 6 (approximately).
- Multiply the remainder (8) by 10: 8 * 10 = 80. Divide it by the divisor (27): 80 / 27 = 2 (approximately).
- Multiply the remainder (26) by 10: 26 * 10 = 260. Divide it by the divisor (27): 260 / 27 = 9 (approximately).
- Multiply the remainder (8) by 10: 8 * 10 = 80. Divide it by the divisor (27): 80 / 27 = 2 (approximately).
- The pattern repeats with 6-2-9-2.
4. The repeating cycle in the decimal expansion of 17/27 is 6292.
Therefore, the repeating cycle of the fraction 17/27 is composed of 4 digits.