Convert 0.27¯¯¯¯¯ to a rational number in simplest form
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number, we can use the following method:
Let x = 0.27¯¯¯¯¯
Multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 27.¯¯¯¯¯
Now we subtract the original equation from the manipulated equation to eliminate the repeating part:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which in this case is 3:
99 ÷ 3 = 33
27 ÷ 3 = 9
So, x = 9/33. Finally, we can simplify further by dividing both numerator and denominator by their GCD, which is 3:
9 ÷ 3 = 3
33 ÷ 3 = 11
Therefore, 0.27¯¯¯¯¯ as a rational number in simplest form is 3/11.
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we can follow these steps:
Step 1: Let x = 0.27¯¯¯¯¯.
Step 2: Multiply both sides of the equation by 100 to remove the repeating decimal:
100x = 27.¯¯¯¯¯.
Step 3: Subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯.
This simplifies to:
99x = 27.
Step 4: Divide both sides of the equation by 99 to solve for x:
x = 27 / 99.
Step 5: Simplify the fraction 27 / 99 by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = (27 ÷ 9) / (99 ÷ 9).
This simplifies to:
x = 3 / 11.
Therefore, the rational number equivalent to 0.27¯¯¯¯¯ in simplest form is 3/11.