Decimal Expansion/Examples

Examples of Decimal Expansions

Decimal Number $234 \cdotp 568$

The number:

$234 \cdotp 568$

is effectively shorthand for:

$2$ hundreds

$3$ tens

$4$ units

plus:

$5$ tenths

$6$ hundredths

$8$ thousandths

Decimal Number $0.207$

The number:

$0 \cdotp 207$

can be expressed as a fraction as:

\(\ds 0 \cdotp 207\)

\(=\)

\(\ds \dfrac 2 {10} + \dfrac 0 {100} + \dfrac 7 {1000}\)

\(\ds \)

\(=\)

\(\ds \dfrac {207} {1000}\)

Decimal Number $23.23$

The number:

$23 \cdotp 23$

can be expressed as a mixed fraction as:

\(\ds 23 \cdotp 23\)

\(=\)

\(\ds 23 + \dfrac 2 {10} + \dfrac 3 {100}\)

\(\ds \)

\(=\)

\(\ds 23 \tfrac {23} {100}\)

Decimal Expansion of $17 / 10$

$\dfrac {17} {10}$ has a decimal expansion of $1 \cdotp 7$.

Decimal Expansion of $9 / 100$

$\dfrac 9 {100}$ has a decimal expansion of $0 \cdotp 09$.

Decimal Expansion of $1 / 6$

$\dfrac 1 6$ has a decimal expansion of $0 \cdotp 1666 \ldots$.

$1 \cdotp 23999 \ldots$ is not a Decimal Expansion

$1 \cdotp 23999 \ldots$

is not a decimal expansion as defined on $\mathsf{Pr} \infty \mathsf{fWiki}$.

This is because it ends in an infinite sequence of $9$s.

The number $1 \cdotp 23999 \ldots$ is equal to, and is best expressed as, $1 \cdotp 24$.