Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯¯ to a rational number in simplest form, we have to set up an equation.
Let x = 0.72¯¯¯¯¯¯
Then 100x = 72.72¯¯¯¯¯¯
Subtracting the first equation from the second equation, we get:
100x - x = 72.72¯¯¯¯¯¯ - 0.72¯¯¯¯¯¯
99x = 72
Dividing both sides of the equation by 99, we get:
x = 72/99
To simplify the fraction 72/99, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (72 ÷ 9) / (99 ÷ 9)
= 8/11
Therefore, the rational number equivalent of 0.72¯¯¯¯¯¯ is 8/11.
To convert a repeating decimal to a rational number in simplest form, we can assign a variable to the repeating decimal and solve for it.
Let's assign x to the repeating decimal: x = 0.72¯¯¯¯¯
Next, we multiply both sides of the equation by 100 to remove the repeating part: 100x = 72.727272...
Now, we subtract the original equation from the multiplied equation to eliminate the repeating part: 100x - x = 72.727272... - 0.72¯¯¯¯¯
Simplifying, we have: 99x = 72.727272... - 0.72¯¯¯¯¯
Subtracting the decimals, we get: 99x = 72.0072
Now, we can simplify both sides of the equation by dividing by 99: x = 72.0072 / 99
To express this as a fraction in simplest form, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 8: x = (72.0072 / 8) / (99 / 8)
Simplifying the numerator and denominator, we get: x = 9.0009 / 12.375
Finally, we can further simplify the fraction by dividing 9.0009 and 12.375 by their greatest common divisor (GCD), which is 0.0009: x = (9.0009 / 0.0009) / (12.375 / 0.0009)
Simplifying the numerator and denominator, we have: x = 10001 / 13750
Therefore, the rational number in simplest form that is equivalent to 0.72¯¯¯¯¯ is 10001/13750.