Converting Decimal Expansion of Rational Number to Fraction/Examples/0.1416

Example of Converting Decimal Expansion of Rational Number to Fraction

The number:

$0. 14 \dot 1 \dot 6$

can be expressed as a fraction as:

\(\ds 0. 14 \dot 1 \dot 6\)

\(=\)

\(\ds \dfrac {1416 - 14} {10^2 \paren {10^2 - 1} }\)

\(\ds \)

\(=\)

\(\ds \dfrac {1402} {9900}\)