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)
bot bro its always wrong
How many digits are in the repeating cycle of 1727
?
one answer only
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
To convert a repeating decimal like 0.82¯¯¯¯¯ to a rational number, we can use a variable, let's say x, and set it equal to 0.82¯¯¯¯¯. To remove the repeating part, we need to multiply both sides of the equation by a suitable power of 10.
The repeating part in 0.82¯¯¯¯¯ is 82. To remove it, we multiply by 100 because there are two digits in the repeating part (82) and we want to move the decimal point two places to the right.
By multiplying both sides of the equation by 100, we get:
100x = 82.82¯¯¯¯¯
Now, let's subtract the original equation from this new equation (100x - x):
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82 (the repeating part cancels out)
Finally, we divide both sides of the equation by 99 to solve for x:
99x/99 = 82/99
x = 82/99
Therefore, the rational number equivalent to 0.82¯¯¯¯¯ is 82/99.
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.
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.