Convert 0.2727... to a rational number in simplest form.(1 point)
Responses
27100
27 over 100
2799
27 over 99
127
1 over 27
311
3 over 11
The correct response is:
27 over 99
Convert 0.5555... to a fraction(1 point)
To convert 0.5555... to a fraction, let's assign x to the repeating decimal:
x = 0.5555...
Then, multiply both sides of the equation by 10 to move the decimal point one place to the right:
10x = 5.5555...
Now, subtract the original equation from the above equation to eliminate the repeating decimal:
10x - x = 5.5555... - 0.5555...
This simplifies to:
9x = 5
Divide both sides of the equation by 9 to solve for x:
x = 5/9
Therefore, 0.5555... can be written as the fraction 5/9.
Convert .33... to a fraction.(1 point)
Responses
33100
33 over 100
310
3 tenths
13
1 third
333
To convert the decimal notation ".33..." to a fraction, let's assign x to the repeating decimal:
x = 0.33...
Then, multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 33.33...
Now, subtract the original equation from the above equation to eliminate the repeating decimal:
100x - x = 33.33... - 0.33...
This simplifies to:
99x = 33
Divide both sides of the equation by 99 to solve for x:
x = 33/99
Simplifying the fraction, we find that both the numerator and denominator can be divided by 33:
x = 1/3
Therefore, the decimal ".33..." can be written as the fraction 1/3.
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
999
999
100
100
99