overview

This page covers converting

• fractions to decimals by long division method

• decimals to fractions by simplifying the equivalent fraction

convert

Decimal numbers are standardized fractions.

The decimal representation of $\frac{1}{2}$ is "$0.5$"

By first principles, $\frac{1}{2}$ is converted to the equivalent fraction $\frac{5}{10}$, which is $0.5$ in decimals.

Note: By first principles, decimals are fractions with denominator $10$, $100$, $1000$ etc. Since the denominator is standardized, it is dropped and is represented with a decimal point.

The fraction $\frac{3}{8}$ is "$0.375$" in decimals.

Considering converting the fraction $\frac{3}{8}$ to decimal.

By first principles, the fraction has to be converted into an equivalent fraction having denominator one of $10$, $100$, $1000$, etc.

$8$ is not a factor of $10$. So the fraction cannot be converted to an equivalent fraction with denominator $10$

$8$ is not a factor of $100$ either. So the fraction cannot be converted to an equivalent fraction with denominator $100$.

$8$ is a factor of $1000=8\times 125$. So, the denominator and numerator are multiplied by $125$.

$\frac{3}{8}=\frac{3\times 125}{8\times 125}=\frac{375}{1000}$

$\frac{375}{1000}=\frac{3}{10}+\frac{7}{100}+\frac{5}{1000}$

$=0.375$ in decimal.

A simplified procedure is devised: By long division method, the decimal is calculated. This is shown in the figure.

**Converting a Fraction to a Decimal -- simplified procedure** : A fraction is converted to the equivalent decimal by long division method.

examples

Convert $\frac{5}{4}$ into decimal.

The answer is "$1.25$".

By long division method,

Convert $\frac{35}{2}$ into decimal.

The answer is "$17.5$".

By long division method,

We learned that the fractions can be converted to decimals. Similarly, decimals can be converted to fractions too.

Convert $6.75$ in to the equivalent fraction

The answer is "$6\frac{3}{4}$"

$6.75$

$=6\frac{75}{100}$

$=6\frac{3}{4}$

summary

**Converting a Fraction to a Decimal -- simplified procedure** : A fraction is converted to the equivalent decimal by long division method.
**Converting a Decimal to a Fraction** : The decimal is represented in its equivalent fraction form and the fraction is simplified.

eg:
$6.75$

$=6\frac{75}{100}$

$=6\frac{3}{4}$

Outline

The outline of material to learn "decimals" is as follows.

Note: *goto detailed outline of Decimals *

• Decimals - Introduction

→ __Decimals as Standard form of Fractions__

→ __Expanded form of Decimals__

• Decimals - Conversion

→ __Conversion between decimals and fractions__

→ __Repeating decimals__

→ __Irrational Numbers__

• Decimals - Arithmetics

→ __Comparing decimals__

→ __Addition & Subtraction__

→ __Multiplication__

→ __Division__

• Decimals - Expressions

→ __Expression Simplification__

→ __PEMA / BOMA__