How many digits are in the repeating cycle of 1727
?(1 point)
The repeating cycle of the decimal representation of 1/1727 can be found by looking for the smallest positive integer n such that 10^n - 1 is divisible by 1727. By trial and error, we find that n = 18. Therefore, the repeating cycle of 1/1727 has 18 digits.
How many digits are in the repeating cycle of 17/27
?(1 point)
To find the repeating cycle of the decimal representation of 17/27, we need to divide 17 by 27. The quotient is 0.6296296296296296. We can see that the repeating cycle is 629. Therefore, the repeating cycle of 17/27 has 3 digits.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by putting a bar over them
by putting a bar over them
by printing them in italics
by printing them in italics
by underlining them
by underlining them
by putting them in parentheses
by putting them in parentheses
The correct response 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
up to seven digits long
up to seven digits long
up to six digits long
up to six digits long
infinitely long
If the denominator of a rational number is 7, the repeating cycle of the decimal representation can be at most 6 digits long. This is because any repeating decimal with a denominator of 7 will have a repeating cycle that is a factor of 6.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
1/27
Start Fraction 1 over 27 end fraction
27/99
Start Fraction 27 over 99 end fraction
27/100
Start Fraction 27 over 100 end fraction
3/11
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can assign a variable x to the repeating decimal:
x = 0.27¯¯¯¯¯
To eliminate the repeating part, we can multiply both sides of the equation by 100 to get:
100x = 27.2727¯¯¯¯¯
Subtracting the original equation from the equation multiplied by 100, we have:
100x - x = 27.2727¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
To find the value of x, we divide both sides of the equation by 99:
x = 27/99
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9, we get:
x = 3/11
Therefore, 0.27¯¯¯¯¯ is equivalent to the rational number 3/11.
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
Responses
10
10
100
100
999
999
1,000