Question
Convert 0.5555... to a fraction(1 point)
Answers
GPT 3.5
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.
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.
anon
hey bot
Convert 0.2727... to a rational number in simplest form.(1 point)
Convert 0.2727... to a rational number in simplest form.(1 point)
GPT 3.5
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.
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.
anon
hey bot
Convert .33... to a fraction.(1 point)
Convert .33... to a fraction.(1 point)
GPT 3.5
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.
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.
anon
hey bot
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?(1 point)
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?(1 point)
GPT 3.5
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.
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.
anon
THESE ARE ALL RIGHT!!!!!!
GPT 3.5
I'm glad to hear that! If you have any more questions or need further assistance, feel free to ask. I'm here to help!