Converting Fractions & Decimals - Pre Algebra

1. A fraction in simplest form has a terminating decimal exactly when its denominator has which prime factors?

   Only $2$s and $5$s (or none). Any other prime factor, such as $3$ or $7$, makes the decimal repeat.

2. Which has a repeating decimal: $\frac{3}{16}$ or $\frac{5}{12}$?

   $\frac{5}{12}$, which equals $0.41\overline{6}$. Its denominator has a factor of $3$, while $16 = 2^4$ gives $0.1875$.

3. What is $\frac{2}{3}$ as a decimal?

   $0.\overline{6}$. Dividing $2$ by $3$ gives $0.666...$, with the $6$ repeating forever.

4. What is $0.07$ as a fraction?

   $\frac{7}{100}$. The $7$ is in the hundredths place, so it is seven hundredths.

5. What is $2.6$ as a mixed number in simplest form?

   $2\frac{3}{5}$. The $0.6$ is $\frac{6}{10} = \frac{3}{5}$.

6. How do you convert a fraction to a decimal?

   Divide the numerator by the denominator. For example, $\frac{3}{4} = 3 \div 4 = 0.75$.

7. What is $\frac{3}{8}$ as a decimal?

   $0.375$. Divide $3$ by $8$.

8. What is $\frac{1}{9}$ as a decimal?

   $0.\overline{1}$. Dividing $1$ by $9$ gives $0.111...$, with the $1$ repeating.

9. What is $0.125$ as a fraction in simplest form?

   $\frac{1}{8}$. Write $\frac{125}{1000}$ and divide both parts by $125$.

10. What is $0.\overline{3}$ as a fraction?

    $\frac{1}{3}$. Dividing $1$ by $3$ gives $0.333...$

11. What is $\frac{7}{20}$ as a decimal?

    $0.35$. Multiply by $\frac{5}{5}$ to get $\frac{35}{100}$.

12. What is $0.45$ as a fraction in simplest form?

    $\frac{9}{20}$. Write $\frac{45}{100}$ and divide both parts by $5$.

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