Final answer:
The repeating decimal 0.373737... can be expressed as the fraction 37/99. The process involves multiplication by 100 to separate out the repeating part, and then subtraction to solve for x.
Step-by-step explanation:
To express the repeating decimal 0.37373737373737... as a fraction, we can use the method for converting repeating decimals to fractions. Let's represent the decimal as x:
x = 0.373737...
To separate out the repeating decimal part, we can multiply x by 100 (since the repeating part is in the 100ths and 1000ths places), which gives:
100x = 37.373737...
Then, subtract the original equation (x) from this result:
100x - x = 37.373737... - 0.373737...
So, 99x = 37
Solving for x, we get:
x = 37 / 99
So, the repeating decimal 0.373737... can be expressed as the fraction 37/99.
Learn more about Repeating Decimal