Converting Decimal Expansion of Rational Number to Fraction/Examples

Examples of Converting Decimal Expansion of Rational Number to Fraction

Decimal Number $0 \cdotp 7 \dot 1 82 \dot 8$

The number:

$0. 7\dot 1 82 \dot 8$

can be expressed as a fraction as:

\(\ds 0. 7 \dot 1 82 \dot 8\)

\(=\)

\(\ds \dfrac {71828 - 7} {10^1 \paren {10^4 - 1} }\)

\(\ds \)

\(=\)

\(\ds \dfrac {71821} {99990}\)

Decimal Number $0 \cdotp 14 \dot 1 \dot 6$

The number:

$0. 14 \dot 1 \dot 6$

can be expressed as a fraction as:

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

\(=\)

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

\(\ds \)

\(=\)

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