Convert 0.72¯¯¯¯¯ to a rational number in simplest form
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the method of converting repeating decimals to fractions.
Let x = 0.72¯¯¯¯¯
We can multiply both sides by 100 to eliminate the repeating decimal:
100x = 72.72¯¯¯¯¯
Now, we subtract the original equation from the equation above to eliminate the decimal part:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides by 99 gives us:
x = 72/99
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
72/99 = (8 * 9)/(11 * 9) = 8/11
Therefore, 0.72¯¯¯¯¯ as a rational number in simplest form is 8/11.
To convert 0.72¯¯¯¯¯ into a rational number in simplest form, we need to set up an equation. Let's set x = 0.72¯¯¯¯¯.
To eliminate the recurring part, multiply both sides of the equation by 100:
100x = 72.72¯¯¯¯¯
Next, subtract the original equation from the new equation:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Now, divide both sides of the equation by 99 to solve for x:
99x / 99 = 72 / 99
x = 72/99
The rational number in simplest form is 72/99.