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Fractions can be converted into decimals by dividing the numerator by the denominator using short division.

\( \frac {3}{8} = 3 \div 8 \)

\(\require{enclose}8\overset{\Large0.375}{\enclose{longdiv}{3.\strut^30\strut^60\strut^40}}\)

\( \frac {3}{8} = 0.375\)

Extra zeros are placed at the end until the decimal answer stops. This is called a finite decimal.

Some fractions you will know as percentages.

\( \frac 12 \) =50\%, \( \frac 34 \)=75%

If it’s not one you know, then divide the numerator by the denominator and then multiply by 100.

\( \frac 38 = 0.375\)
\( 0.375 \times 100\) = 37.5%

A recurring decimal exists when decimal numbers repeat forever.

\( \frac 13 = 0.3333333333…\) the decimal never ends.

Dot notation is used with recurring decimals.

0.33333… is written as \(0.\dot{3}\)

The dot above the 3 shows that the 3 keeps repeating.

0.255255255… can be written as \(0.\dot{2}5\dot{5}\)

The dot above the 2 and the 5 shows that the numbers between the dots, 255 keep repeating.

Change \(\frac13\) to a decimal.

Solution

• \(\frac13 = 1\div3\)

• ��(�������ܾ��������Գ����Dz���3���DZ��������ٵ�������������0.3333…}������Գ����Dz�������DzԲ��徱������1.�����ٰ��ٰܳ�10�����ٰ��ٰܳ�10�����ٰ��ٰܳ�10�����ٰ��ٰܳ�10����…\)

• \(\frac13 = 0.333333…\) the decimal never ends.

Using dot notation…

• 0.3333… is written as \(0.\dot{3}\)