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How many digits are in the repeating cycle of 1727

?(1 point)

13 answers

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
To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000, not 1,000.

So the correct response is:

1,000
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses

1,000
1,000

999
999

100
100

99
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 99.

So the correct response is:

99