Write the following infinite decimal expansion as a fraction

Question

0.35

Answer 1

To express the decimal \(0.35\) as a fraction, we observe that it can be written as follows:

\[ 0.35 = \frac{35}{100} \]

Next, we simplify the fraction. We find the greatest common divisor (GCD) of 35 and 100. The GCD of \(35\) and \(100\) is \(5\).

Now, we divide both the numerator and the denominator by their GCD:

\[ \frac{35 \div 5}{100 \div 5} = \frac{7}{20} \]

Thus, the decimal \(0.35\) expressed as a fraction in simplest form is:

\[ \boxed{\frac{7}{20}} \]