Convert 0.5555... to a fraction(1 point)
To convert 0.5555... to a fraction, we can let x = 0.5555... and multiply it by 10 to eliminate the repeating decimal:
10x = 5.5555...
Next, we subtract x from 10x:
10x - x = 5.5555... - 0.5555...
This simplifies to:
9x = 5
To solve for x, we divide both sides of the equation by 9:
x = 5/9
Therefore, 0.5555... as a fraction is 5/9.
To convert 0.2727... to a rational number in simplest form, we can let x = 0.2727... and multiply it by 100 to eliminate the repeating decimal:
100x = 27.2727...
Next, we subtract x from 100x:
100x - x = 27.2727... - 0.2727...
This simplifies to:
99x = 27
To solve for x, we divide both sides of the equation by 99:
x = 27/99
Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = (27/9) / (99/9)
x = 3/11
Therefore, 0.2727... as a rational number in simplest form is 3/11.
To convert 0.33... to a fraction, we can let x = 0.33... and multiply it by 100 to eliminate the repeating decimal:
100x = 33.33...
Next, we subtract x from 100x:
100x - x = 33.33... - 0.33...
This simplifies to:
99x = 33
To solve for x, we divide both sides of the equation by 99:
x = 33/99 = 1/3
Therefore, 0.33... as a fraction is equal to 1/3.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
This is because the repeating cycle of three digits in the decimal can be expressed as a fraction with the numerator being the repeating digits and the denominator being a string of nines with the same number of digits as the repeating cycle.
For example, if the repeating cycle is 123, the fraction equivalent would be 123/999.
Therefore, a repeating decimal with a repeating cycle of three digits will convert to a rational number with a denominator of 999.
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Convert 0.2727... to a rational number in simplest form.(1 point)
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Convert .33... to a fraction.(1 point)
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If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?(1 point)
THESE ARE ALL RIGHT!!!!!!
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To convert the recurring decimal 0.5555... to a fraction, we need to follow these steps:
Step 1: Let x = 0.5555...
Step 2: Multiply both sides of the equation by 10 to shift the decimal place to the right:
10x = 5.5555...
Step 3: Subtract the original equation (x) from the equation obtained in the previous step (10x) to eliminate the decimal part:
10x - x = 5.5555... - 0.5555...
This simplifies to:
9x = 5
Step 4: Divide both sides of the equation by 9 to solve for x:
x = 5/9
Hence, 0.5555... is equivalent to the fraction 5/9.