Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
2799
Start Fraction 27 over 99 end fraction
127
Start Fraction 1 over 27 end fraction
27100
Start Fraction 27 over 100 end fraction
311
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)
100
10
1,000
999
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 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)
99
999
1,000
100
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 99.
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we can represent the repeating decimal as a fraction.
Let's denote 0.27¯¯¯¯¯ as x.
To remove the repeating decimal, we multiply both sides of the equation by 100, since there are two digits after the decimal point:
100x = 27.¯¯¯¯¯
100x = 27 + 0.27¯¯¯¯¯ (adding x to both sides to eliminate the repeating decimal)
100x = 27 + x (simplifying the decimal on the right side)
Now, let's solve for x:
100x - x = 27
99x = 27
x = 27/99
So, 0.27¯¯¯¯¯ can be expressed as the fraction 27/99 in simplest form.
Therefore, the correct answer is:
Start Fraction 27 over 99 end fraction.
To convert a repeating decimal into a rational number in simplest form, you need to identify the repeating pattern and represent it as a fraction.
In this case, the number is 0.27¯¯¯¯¯, where the bar signifies the repeating pattern. To convert this to a fraction, you can follow these steps:
1. Let x = 0.27¯¯¯¯¯.
2. Multiply both sides of the equation by 100 to get rid of the repeating decimal:
100x = 27.27¯¯¯¯¯
3. Subtract the original equation from the equation above to eliminate the repeating pattern:
100x - x = 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27 (subtracting the decimal parts cancels out the repeating pattern)
4. Simplify the equation by dividing both sides by 99:
x = 27/99
Therefore, 0.27¯¯¯¯¯ is equal to the fraction 27/99, which is already simplified.