how to find Convert 0.27¯¯¯¯¯
to a rational number in simplest form. if the answer is 3/11
To find a rational number equivalent to 0.27¯¯¯¯¯, we can write the recurring decimal as a fraction and simplify it to its simplest form.
Let x = 0.27¯¯¯¯¯
Multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 27.¯¯¯¯¯
Now we subtract the original equation from the second equation to eliminate the repeating decimal:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Divide both sides of the equation by 99 to isolate x:
x = 27/99
We can simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = (27/9) / (99/9)
x = 3/11
Therefore, the rational number equivalent to 0.27¯¯¯¯¯ in its simplest form is 3/11.
To find the rational representation of the repeating decimal 0.27¯¯¯¯¯ in its simplest form, follow these steps:
Step 1: Assign a variable to the repeating decimal.
Let x = 0.27¯¯¯¯¯
Step 2: Multiply both sides of the equation by 100 to eliminate the repeating decimal.
100x = 27.27777¯¯¯¯¯
Step 3: Subtract the original equation from the newly obtained equation to eliminate the repeating decimal.
100x - x = 27.27777¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Step 4: Divide both sides of the equation by 99 to isolate the variable.
99x/99 = 27/99
x = 3/11
Therefore, the rational representation of 0.27¯¯¯¯¯ is 3/11.