Convert 0.09¯¯¯¯¯
to a rational number in simplest form.
The repeating decimal 0.09¯¯¯¯¯ can be written as 0.0999999...To convert it to a rational number, we can call it x and subtract it from 10x.
10x - x = 9.99999... - 0.0999999...
9x = 9.9
x = 9.9 / 9
x = 1.1
Therefore, 0.09¯¯¯¯¯ can be written as the rational number 1.1 in simplest form.
To convert 0.09¯¯¯¯¯ to a rational number in simplest form, we need to represent the repeating decimal as a fraction.
Let x = 0.09¯¯¯¯¯
To remove the repeating decimal part, we can multiply both sides of the equation by 10 (since there is one digit repeating after the decimal point):
10x = 0.99¯¯¯¯¯
Next, we subtract the original equation from this new equation to eliminate the repeating part:
10x - x = 0.99¯¯¯¯¯ - 0.09¯¯¯¯¯
Simplifying,
9x = 0.9
Dividing both sides by 9,
x = 0.1
So, 0.09¯¯¯¯¯ can be represented as the fraction 1/10 in simplest form.