Convert 0.09¯¯¯¯¯ to a rational number in simplest form
To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number, we can set it equal to the variable x and multiply both sides of the equation by 100 to remove the repeating decimal.
0.09¯¯¯¯¯ = x
Multiplying both sides by 100 gives:
100(0.09¯¯¯¯¯) = 100x
9.¯¯¯¯¯ = 100x
Now, let's subtract the original equation from the above equation:
100x - x = 9.¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9
Dividing both sides by 99, we get:
x = 9/99
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, we get:
x = 1/11
Therefore, the rational number equivalent to 0.09¯¯¯¯¯ is 1/11.
To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number in simplest form, we can use the concept of infinite geometric series.
Let x = 0.09¯¯¯¯¯
Multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 9.09¯¯¯¯¯
Next, subtract the original equation from the multiplied equation to eliminate the repeating decimal:
100x − x = 9.09¯¯¯¯¯ − 0.09¯¯¯¯¯
99x = 9
Now, divide both sides of the equation by 99 to solve for x:
x = 9/99
This fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 9:
x = (9 ÷ 9) / (99 ÷ 9)
= 1/11
Therefore, the rational number equivalent of 0.09¯¯¯¯¯ in simplest form is 1/11.