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
127
Start Fraction 1 over 27 end fraction
2799
Start fraction 27 over 100 end fraction
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
Responses
1,000
1,000
100
100
10
10
999
1,000
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
1,000
1,000
100
100
999
999
99
99
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we can use the following 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:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Step 4: Divide both sides of the equation by 99 to solve for x:
x = 27/99
Step 5: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor:
x = 3/11
So, when 0.27¯¯¯¯¯ is converted to a rational number in simplest form, it is equal to 3/11.
To convert a recurring decimal like 0.27¯¯¯¯¯ to a rational number in simplest form, we need to identify the repeating pattern and express it as a fraction.
In this case, the recurring pattern is the "27" after the decimal point. To express this as a fraction, we can set up an equation where x equals the recurring decimal:
x = 0.272727...
Next, we multiply the equation by 100 (to move the decimal point two places to the right):
100x = 27.272727...
Now, to eliminate the repeating pattern, we subtract the original equation from the multiplied equation:
100x - x = 27.272727... - 0.272727...
99x = 27
x = 27/99
Simplifying this fraction further, we can divide the numerator and denominator by their greatest common divisor, which is 9:
x = (27/9)/(99/9)
x = 3/11
Therefore, the rational form of 0.27¯¯¯¯¯ is 3/11.