Convert 0.27¯¯¯¯¯ to a rational number in simplest form.
Step 1: Let x = 0.27¯¯¯¯¯
Step 2: Multiply both sides of the equation by 100 to remove the decimal: 100x = 27.¯¯¯¯¯
Step 3: Subtract x from both sides: 100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
This simplifies to 99x = 27.
Step 4: Divide both sides by 99: 99x/99 = 27/99
This simplifies to x = 27/99.
Therefore, 0.27¯¯¯¯¯ as a rational number in simplest form is 27/99.
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can use a system of equations. Let's denote the repeating part by x:
x = 0.27¯¯¯¯¯
Multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 27.¯¯¯¯¯
Now, subtract the original equation from this new equation to eliminate the repeating part:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
Simplifying the right side gives:
99x = 27
Now, divide both sides of the equation by 99:
x = 27 / 99
This fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator, which is 9. Divide both the numerator and denominator by 9:
x = 27 / 99 = 3 / 11
Therefore, the rational form of the repeating decimal 0.27¯¯¯¯¯ is 3/11.