Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
311
Start Fraction 3 over 11 end fraction
27100
Start Fraction 27 over 100 end fraction
2799
Start Fraction 27 over 99 end fraction
127
Start Fraction 27 over 100 end fraction
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can use the fact that any repeating decimal can be expressed as a fraction. Let's represent the repeating decimal 0.27¯¯¯¯¯ as x.
To eliminate the repeating decimal, we can multiply both sides of the equation by 100, which moves the decimal two places to the right:
100x = 27.¯¯¯¯¯
Next, we can subtract x from 100x to eliminate the repeating decimal:
100x - x = 27.¯¯¯¯¯ - 0.¯¯¯¯¯
99x = 27
Dividing both sides of the equation by 99:
x = 27/99
So, the rational number in simplest form that is equivalent to the repeating decimal 0.27¯¯¯¯¯ is:
Start Fraction 27 over 99 end fraction.