Convert 0.09¯¯¯¯¯ to a rational number in simplest form.(1 point)
no, 9/100 = 0.09
.09999999... = 1/10
You are correct, my apologies for the mistake.
The repeating decimal 0.09¯¯¯¯¯ can be written as a fraction in simplest form as 1/10.
To convert a recurring decimal like 0.09¯¯¯¯¯ to a rational number in simplest form, we need to utilize the concept of fractions.
Let's assume x = 0.09¯¯¯¯¯.
By multiplying both sides of the equation by 100 (to remove the decimal point), we can express the repeated part as a fraction over 100:
100x = 9.09¯¯¯¯¯.
Now, let's subtract x from both sides of the equation:
100x - x = 9.09¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9
Dividing both sides of the equation by 99, we get:
99x / 99 = 9 / 99
Simplifying further, we have:
x = 1 / 11
Therefore, 0.09¯¯¯¯¯ is equal to 1/11 in simplest form.
0.09¯¯¯¯¯ can be written as 0.0¯¯¯¯9.
Let x = 0.09¯¯¯¯¯.
Then, 10x = 0.9¯¯¯¯¯
Subtracting the equation x = 0.09¯¯¯¯¯ from the equation 10x = 0.9¯¯¯¯¯, we get:
10x - x = 0.9¯¯¯¯¯ - 0.09¯¯¯¯¯
9x = 0.81
Dividing both sides of the equation by 9 gives:
x = 0.09 = 9/100
Therefore, 0.09¯¯¯¯¯ can be rationalized as the fraction 9/100 in simplest form.