Express each of the following as a fraction or mixed number in simplest form: 1.9, 3.5, 0.46, 3.08.

Steps to Solve

1. Convert the decimal to a fraction

   For each decimal, express it as a fraction by placing the number over 1 and then multiplying the numerator and denominator by a power of 10 based on the number of decimal places.

   • For $1.9$, since there is one decimal place: $$ 1.9 = \frac{1.9}{1} = \frac{1.9 \times 10}{1 \times 10} = \frac{19}{10} $$

   • For $3.5$, since there is one decimal place: $$ 3.5 = \frac{3.5}{1} = \frac{3.5 \times 10}{1 \times 10} = \frac{35}{10} $$

   • For $0.46$, since there are two decimal places: $$ 0.46 = \frac{0.46}{1} = \frac{0.46 \times 100}{1 \times 100} = \frac{46}{100} $$

   • For $3.08$, since there are two decimal places: $$ 3.08 = \frac{3.08}{1} = \frac{3.08 \times 100}{1 \times 100} = \frac{308}{100} $$

2. Simplify the fractions

   Reduce each fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).

   • For $\frac{19}{10}$, it is already in simplest form.

   • For $\frac{35}{10}$, the GCD is 5: $$ \frac{35 \div 5}{10 \div 5} = \frac{7}{2} $$

   • For $\frac{46}{100}$, the GCD is 2: $$ \frac{46 \div 2}{100 \div 2} = \frac{23}{50} $$

   • For $\frac{308}{100}$, the GCD is 4: $$ \frac{308 \div 4}{100 \div 4} = \frac{77}{25} $$

3. Convert to mixed numbers if necessary

   Convert any improper fractions (numerator larger than denominator) into mixed numbers.

   • $\frac{7}{2} = 3 \frac{1}{2}$
   • $\frac{77}{25}$ remains as it is not improper here.