Decimal-Fraction Conversion Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Decimal-Fraction Conversion.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept 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. $\frac{3}{4}$ and $0.75$ are the same amount—just different notation.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Decimal-fraction conversion is renaming the same number using base-ten fraction units.

Common stuck point: The procedure for decimal-fraction conversion is the easy part; the trap is using 10 as the denominator for every decimal. Asking "Does the new form land at the same point on the number line?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does the new form land at the same point on the number line?

Worked Examples

Example 1

easy

Convert

\frac{7}{8}

to a decimal.

Answer

0.875

First step

Divide the numerator by the denominator:

7 \div 8

Full solution

2
$7.000 \div 8$ : $8$ goes into $70$ eight times ( $64$ ), remainder $6$ . Bring down: $60$ . $8$ into $60$ is $7$ ( $56$ ), remainder $4$ . Bring down: $40$ . $8$ into $40$ is $5$ , remainder $0$ .
3
Result: $7 \div 8 = 0.875$ .

To convert a fraction to a decimal, perform long division of the numerator by the denominator. When the remainder reaches zero, the decimal terminates. A fraction terminates when the denominator (in lowest terms) has only factors of 2 and/or 5.

Example 2

medium

Convert

0.36

to a fraction in simplest form.

Example 3

medium

Convert

\frac{11}{25}

to a decimal.

Example 4

medium

Convert

0.6

to a fraction in simplest form by showing both forms.

Example 5

medium

Pattern: convert

\frac{1}{8}, \frac{2}{8}, \frac{3}{8}

to decimals and look for the step.

Example 6

hard

A recipe calls for

0.375

cup of sugar. Express this as a fraction of a cup.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Convert

\frac{3}{5}

to a decimal.

Example 2

hard

Convert

0.125

to a fraction, then determine whether

\frac{1}{8}

and

0.125

are equal by comparing their decimal equivalents.

Example 3

easy

Write

0.5

as a fraction in simplest form.

Example 4

easy

Write

\frac{3}{4}

as a decimal.

Example 5

easy

Write

0.25

as a fraction in simplest form.

Example 6

easy

Write

\frac{1}{2}

as a decimal.

Example 7

easy

Write

0.7

as a fraction.

Example 8

easy

Write

\frac{1}{5}

as a decimal.

Example 9

easy

Write

0.6

as a fraction in simplest form.

Example 10

easy

Write

\frac{1}{4}

as a decimal.

Example 11

medium

Write

0.125

as a fraction in simplest form.

Example 12

medium

Write

\frac{3}{8}

as a decimal.

Example 13

medium

Write

\frac{2}{3}

as a decimal (round to hundredths).

Example 14

medium

Write

1.4

as a mixed number in simplest form.

Example 15

medium

Order from least to greatest:

0.6

\frac{1}{2}

\frac{3}{5}

Example 16

medium

Write

0.04

as a fraction in simplest form.

Example 17

medium

Write

\frac{7}{20}

as a decimal.

Example 18

medium

Write

0.45

as a fraction in simplest form.

Example 19

medium

Write

\frac{5}{8}

as a decimal.

Example 20

challenge

A student claims

\frac{1}{3}=0.3

. Use a benchmark to show this is wrong and give a better value.

Example 21

challenge

Convert

0.\overline{6}

(repeating) to a fraction.

Example 22

challenge

Which is larger and by how much:

\frac{5}{8}

0.6

Example 23

easy

Write

0.9

as a fraction in simplest form.

Example 24

easy

Write

\frac{2}{5}

as a decimal.

Example 25

easy

Write

\frac{9}{10}

as a decimal.

Example 26

easy

Write

0.2

as a fraction in simplest form.

Example 27

easy

Write

0.01

as a fraction.

Example 28

medium

Write

0.075

as a fraction in simplest form.

Example 29

medium

Convert

\frac{9}{40}

to a decimal.

Example 30

medium

Write

0.16

as a fraction in simplest form.

Example 31

medium

Convert

\frac{7}{8}

to a decimal.

Example 32

medium

Write

\frac{11}{20}

as a decimal.

Example 33

medium

Convert

0.85

to a fraction in simplest form.

Example 34

medium

Order from least to greatest:

0.7

\frac{2}{3}

\frac{3}{4}

Example 35

hard

Convert

\frac{5}{6}

to a decimal, rounded to thousandths.

Example 36

hard

Write

0.008

as a fraction in simplest form.

Example 37

hard

Write

\frac{17}{50}

as a decimal.

Example 38

hard

Which is larger:

\frac{7}{12}

0.6

Example 39

challenge

Convert the repeating decimal

0.\overline{27}

to a fraction in simplest form.

Example 40

challenge

A fraction

\frac{p}{q}

with

\gcd(p,q)=1

has a terminating decimal exactly when

q

's prime factors are only

2

s and

5

s. Which of

\frac{3}{16}

\frac{4}{15}

\frac{7}{20}

terminate?

← Back to Decimal-Fraction Conversion Formula Explained Practice Mode

Related Concepts

Fractions Decimals Percent of a Number Decimal Operations

Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsdecimals