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