Question

To convert 0.82¯¯¯¯¯
to a rational number, you would set x
equal to 0.82¯¯¯¯¯
and then multiply both sides of the equation by what number?(1 point)

Answer 1

To convert the recurring decimal 0.82¯¯¯¯¯ to a rational number, we can set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 100 (since there are two digits recurring after the decimal point). This gives us:

100x = 82.82¯¯¯¯¯

Now we can subtract x from both sides:

100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯

99x = 82

Finally, we divide both sides by 99 to solve for x:

x = 82/99

Therefore, multiplying both sides of the equation by 100 converts 0.82¯¯¯¯¯ to the rational number 82/99.

Answer 2

How many digits are in the repeating cycle of 1727
?

one answer only

Answer 3

The repeating cycle of 1727 is the number 72. Therefore, there are 2 digits in the repeating cycle of 1727.

Answer 4

How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)

infinitely long

up to seven digits long

up to six digits long

any finite length

Answer 5

If the denominator of the rational number is 7, the repeating decimal can be infinitely long. This is because when we divide a number by 7, the remainder can repeat indefinitely as we continue the division process.

Answer 6

bot bro its always wrong