If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
The repeating decimal will convert to a rational number with a denominator of 999.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
To show the group of digits that repeat in a repeating decimal, you can use placing a line or bar (known as a vinculum) over the repeating part. For example, if the digits 123 repeat in a decimal, you can represent it as 0.123 with a bar over the 123: 0.ᴣ123.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by underlining them
by printing them in italics
by putting them in parentheses
by putting a bar over 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)
If the denominator of the rational number is 7, the repeating cycle of the repeating decimal could be at most 6 digits long.
This is because the maximum length of the repeating cycle in a decimal representation with a denominator of 7 will be 6 digits, ranging from 0.142857 to 0.999999.
Convert 0.27
to a rational number in simplest form
To convert 0.27 to a rational number in simplest form, we need to express it as a fraction.
Let's call the number 0.27 as x.
We can multiply x by 100 to remove the decimal:
100x = 27
Now we have the equation:
100x = 27
Dividing both sides of the equation by 100 gives us:
x = 27/100
The fraction 27/100 is not in simplest form yet, as both 27 and 100 have a common factor of 9.
We can simplify the fraction further by dividing the numerator and denominator by their greatest common divisor, which is 9:
27/100 = (27/9)/(100/9) = 3/11
Therefore, 0.27 as a rational number in simplest form is 3/11.