Bot, 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 a parenthesis to enclose the repeating digits. For example, if the decimal pattern is 0.142857142857..., you can show it as 0.142857(142857...). By doing so, you indicate that the digits 142857 repeat infinitely.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
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
by underlining them
by putting them in parentheses
by putting them in parentheses
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
infinitely long
infinitely long
up to seven digits long
up to seven digits long
up to six digits long
up to six digits long
any finite length
If the denominator of a rational number is 7, the repeating cycle of its repeating decimal can be up to six digits long.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.27¯¯¯¯¯¯ to a rational number in simplest form, we can use the following steps:
Let x = 0.27¯¯¯¯¯¯
Multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 27.¯¯¯¯¯¯
Subtract x from both sides of the equation:
100x - x = 27.¯¯¯¯¯¯ - 0.27¯¯¯¯¯¯
99x = 27
Divide both sides of the equation by 99:
x = 27/99
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (which is 9):
x = 3/11
Therefore, 0.27¯¯¯¯¯¯ is equivalent to the rational number 3/11 in its simplest form.
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)
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 1000 (since there are 3 repeating digits).
So the multiplication would be:
1000x = 264.264¯¯¯¯¯¯¯¯
This eliminates the repeating decimal.
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
100
100
1,000
1,000
10
10
999