How many digits are in the repeating cycle of 1727
To find the repeating cycle of the decimal representation of 1727, we can divide 1 by 1727:
1 ÷ 1727 = 0.00057907...
The decimal representation of 1 divided by 1727 is a non-repeating decimal, and therefore does not have a repeating cycle.
How many digits are in the repeating cycle of 17/27
To find the repeating cycle of the fraction 17/27, we can perform long division:
____0. (no repeating part here)
27 | 17. (decimal part starts here)
-16
10
- 9
1
The decimal representation of 17/27 is approximately 0.629629629..., where the digits 6, 2, and 9 form the repeating cycle. Thus, the repeating cycle of 17/27 contains 3 digits.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by putting them in parentheses
by putting them in parentheses
by printing them in italics
by printing them in italics
by putting a bar over them
by putting a bar over them
by underlining them
The correct answer is:
by putting a bar over them
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)
Responses
any finite length
any finite length
infinitely long
infinitely long
up to six digits long
up to six digits long
up to seven digits long
If the denominator of a rational number is 7, then the repeating cycle of the corresponding repeating decimal can be up to six digits long.
This is because when we divide a number by 7, the remainder can be any number from 0 to 6. So, the repeating cycle can consist of at most six different digits.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can set it up as an algebraic equation.
Let x = 0.27¯¯¯¯¯.
We can multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 27.¯¯¯¯¯
Next, we can subtract the original equation from the multiplied equation:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
This simplifies to:
99x = 27
Now we can solve for x:
x = 27/99
To simplify this fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:
x = (27/9) / (99/9)
x = 3/11
Therefore, the rational number equivalent to the repeating decimal 0.27¯¯¯¯¯ in simplest form is 3/11.