how many digits are in the repeating cycle of 17 27
To find the repeating cycle of a fraction, we can convert it into a decimal form.
Let's start with 17/27.
17 ÷ 27 = 0.629629...
From this division, we can see that the repeating cycle of digits is 629.
Therefore, the repeating cycle of digits in the decimal form of 17/27 is 3 digits long.
Convert 0.8 repeating to a rational number
To convert 0.8 repeating to a rational number, we can use the concept of a repeating decimal.
Let x = 0.8 recurring.
We can multiply both sides of the equation by 10 to get:
10x = 8.8 recurring.
Now, subtract x from both sides to eliminate the repeating decimal:
10x - x = 8.8 recurring - 0.8 recurring
9x = 8
Divide both sides by 9:
9x/9 = 8/9
x = 8/9
Therefore, the rational number equivalent to 0.8 recurring is 8/9.
To determine the number of digits in the repeating cycle of a decimal representation of a fraction, we need to find the denominator of the fraction.
In this case, we have the fraction 17/27. The denominator is 27.
To find the number of digits in the repeating cycle, we need to divide 1 by the denominator and observe the pattern that emerges. Let's do the division:
1 ÷ 27 = 0.037037037...
We can see that the repeating cycle is "037", which has 3 digits.
So, the repeating cycle of the decimal representation of 17/27 has 3 digits.