Practice Decimal-Fraction Conversion in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Converting between fraction form and decimal form of a number: divide numerator by denominator for fraction-to-decimal, and use place value to go the other way.

Fractions and decimals are two ways to write the same number. 34\frac{3}{4} and 0.750.75 are the same amountβ€”just different notation.

Showing a random 20 of 50 problems.

Example 1

medium
Order from least to greatest: 0.60.6, 12\frac{1}{2}, 35\frac{3}{5}.

Example 2

easy
Write 0.60.6 as a fraction in simplest form.

Example 3

easy
Convert 35\frac{3}{5} to a decimal.

Example 4

hard
Write 1750\frac{17}{50} as a decimal.

Example 5

medium
Write 720\frac{7}{20} as a decimal.

Example 6

medium
Write 0.160.16 as a fraction in simplest form.

Example 7

challenge
A fraction pq\frac{p}{q} with gcd⁑(p,q)=1\gcd(p,q)=1 has a terminating decimal exactly when qq's prime factors are only 22s and 55s. Which of 316\frac{3}{16}, 415\frac{4}{15}, 720\frac{7}{20} terminate?

Example 8

easy
Write 34\frac{3}{4} as a decimal.

Example 9

medium
Write 0.0750.075 as a fraction in simplest form.

Example 10

medium
Convert 940\frac{9}{40} to a decimal.

Example 11

easy
Write 0.20.2 as a fraction in simplest form.

Example 12

medium
Convert 78\frac{7}{8} to a decimal.

Example 13

easy
Fill in the blank: 0.08=?1000.08 = \frac{?}{100}.

Example 14

challenge
Which is larger and by how much: 58\frac{5}{8} or 0.60.6?

Example 15

easy
Write 0.250.25 as a fraction in simplest form.

Example 16

medium
Write 0.040.04 as a fraction in simplest form.

Example 17

easy
Write 15\frac{1}{5} as a decimal.

Example 18

challenge
Convert the repeating decimal 0.27β€Ύ0.\overline{27} to a fraction in simplest form.

Example 19

medium
Write 0.450.45 as a fraction in simplest form.

Example 20

medium
Write 1.41.4 as a mixed number in simplest form.