Convert .33... to a fraction
To convert .33... to a fraction, we need to identify the repeating pattern. The pattern in this case is 3.
Let's say x = 0.33...
Then, 100x = 33.33...
Now, let's subtract the two equations:
(100x - x) = (33.33... - 0.33...)
99x = 33
x = 33/99
Simplifying the fraction, we can divide both the numerator and denominator by 33:
x = 1/3
Therefore, .33... is equal to 1/3 in fraction form.
To convert the recurring decimal .33... to a fraction, we need to identify the pattern in the decimal.
Let's call the number x, so we have:
x = .33...
To remove the recurring part, we can multiply x by a power of 10.
We multiply both sides of the equation by 100:
100x = 33.33...
Now, let's try to align the decimal points:
100x = 33.33...
= 33 + .33...
Since the decimal part .33... is the same as x, we can substitute it:
100x = 33 + x
Now, rearrange the equation to solve for x:
99x = 33
Divide both sides of the equation by 99:
x = 33/99
So, the fraction equivalent to the recurring decimal .33... is 33/99.
However, we can simplify this fraction further. Both 33 and 99 have a common factor of 33:
33/33 ÷ 99/33 = 1/3
Therefore, the simplified fraction for .33... is 1/3.