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

PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

Book Free Demo

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