.93 Repeating as a Fraction
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is .93 repeating, which can be written as 0.939393... . But what is .93 repeating as a fraction?
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use the following steps:
- Let x be the repeating decimal: In this case, let x = 0.939393...
- Multiply x by 100: This will shift the decimal point two places to the right, which will help us isolate the repeating part. 100x = 93.939393...
- Subtract x from 100x: This will eliminate the non-repeating part of the decimal. 100x - x = 93
- Solve for x: Divide both sides of the equation by 99, which is the number of times the decimal was shifted. x = 93/99
Simplifying the Fraction
The fraction 93/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 93 and 99 is 3.
93 ÷ 3 = 31 99 ÷ 3 = 33
So, the simplified fraction is:
x = 31/33
.93 Repeating as a Fraction
Therefore, .93 repeating as a fraction is equal to 31/33.
