Period of decimal expansion — lesson. Mathematics State Board, Class 9.

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The number of repeating decimals in the decimal expansion of the rational number is called the period of the decimal.

Example:

Verify

$7 = 6. \bar{9}$

Let

$x = 6. \bar{9} = 6.9999...$

As the period of the circle for

$x$ is one(only the number

$9$ repeating), multiply the number by

$10$ .

We have

$10x = 69.9 999...$

Subtracting

$x$ from

$10x$ ,

$\begin{array}{l} 10x - x = 69.9 999... - 6.999... \\ 9 x = 63 \\ x = \frac{63}{9} \\ x = 7 \end{array}$

Thus, we have

$x = 6. \bar{9}$ and

$x = 7$ . This implies

$7 = 6. \bar{9}$ .

Did you find an error?

3. Period of decimal expansion