Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
127
Start Fraction 1 over 27 end fraction
2799
Start Fraction 27 over 99 end fraction
27100
Start Fraction 27 over 100 end fraction
311
Start Fraction 27 over 100 end fraction
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can represent it as a fraction. Let's assign a variable x to 0.27¯¯¯¯¯.
We can start by multiplying both sides of the equation x = 0.27¯¯¯¯¯ by 100 to get rid of the repeating decimal:
100x = 27.27¯¯¯¯¯
Next, we subtract x from both sides of the equation to eliminate the repeating part:
100x - x = 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯
simplifies to:
99x = 27
Dividing both sides of the equation by 99 gives us:
x = 27/99
This fraction can be simplified further. Both the numerator and denominator are divisible by 9. By dividing both by 9, we get:
x = 3/11
Therefore, the rational number representation of 0.27¯¯¯¯¯ in simplest form is 3/11.