Convert 0.27¯¯¯¯¯
to a rational number in simplest form. (1 point)
A. 27/99
B. 12/7
C. 27/100
D. 3/11
wrong
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 eliminate the repeating decimal:
100x = 27.¯¯¯¯¯.
Step 3: Subtract x from both sides of the equation to eliminate the repeating decimal:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯.
Simplifying the left side gives us:
99x = 27.
Step 4: Divide both sides of the equation by 99 to solve for x:
99x/99 = 27/99.
Simplifying the fraction on the right side gives us:
x = 27/99.
Therefore, the answer is A. 27/99.
To convert the recurring decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can use the method of converting repeating decimals to fractions.
Let x = 0.27¯¯¯¯¯.
Step 1: Multiply both sides of the equation by 100 (to get rid of the recurring decimal):
100x = 27.272727...
Step 2: Subtract the original equation from the equation in Step 1 to eliminate the recurring part:
100x - x = 27.272727... - 0.27¯¯¯¯¯
99x = 27
Step 3: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (in this case, 3):
99x = 27
Divide both sides by 3:
33x = 9
Step 4: Solve for x by dividing both sides by 33:
x = 9/33 = 3/11
Therefore, the rational number equivalent to the recurring decimal 0.27¯¯¯¯¯ in simplest form is D. 3/11.
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number, we can assign a variable to the repeating portion. Let x = 0.27¯¯¯¯¯.
To eliminate the repeating portion, we can multiply both sides of the equation by 100 to shift the decimal point two places to the right:
100x = 27.¯¯¯¯¯
Next, subtract the original equation from the shifted equation to eliminate the repeating portion:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Now, divide both sides of the equation by 99 to solve for x:
x = 27/99
Therefore, the rational number in simplest form that is equivalent to 0.27¯¯¯¯¯ is 27/99.
The correct answer is A. 27/99.