Decimals : Conversion of Fraction and Decimals

maths > decimals

Conversion of Fraction and Decimals

what you'll learn...

overview

This page covers converting

• fractions to decimals by long division method

• decimals to fractions by simplifying the equivalent fraction

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Decimal numbers are standardized fractions.

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

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

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

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

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

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

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

$8$ $8$ is a factor of $1000 = 8 \times 125$ $1000 = 8xx125$ . So, the denominator and numerator are multiplied by $125$ $125$ .

$\frac{3}{8} = \frac{3 \times 125}{8 \times 125} = \frac{375}{1000}$ $3/8 = (3xx125)/(8xx125) = 375/1000$

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

$= 0.375$ $=0.375$ in decimal.
$division to convert fraction to decimal$ 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 $\frac{5}{4}$ $5/4$ into decimal.
The answer is " $1.25$ $1.25$ ".

By long division method,

Convert $\frac{35}{2}$ $35/2$ into decimal.
The answer is " $17.5$ $17.5$ ".

By long division method,

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

Convert $6.75$ $6.75$ in to the equivalent fraction
The answer is " $6 \frac{3}{4}$ $6 3/4$ "
$6.75$ $6.75$
$= 6 \frac{75}{100}$ $= 6 75/100$
$= 6 \frac{3}{4}$ $= 6 3/4$

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: $6.75$ $6.75$
$= 6 \frac{75}{100}$ $= 6 75/100$
$= 6 \frac{3}{4}$ $= 6 3/4$

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