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Have a play with decimal numbers yourself:

View Larger Large and Small So, our Decimal System lets us write numbers as large or as small as we want, using the decimal point. Digits can be placed to the left or right of a decimal point, to indicate values greater than one or less than one. The decimal point is the most important part of a Decimal Number. Without it, we would be lost ... and not know what each position meant. 17 . 591

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q <--some integer

Conversion decimal to the form p / q.

1) Obtain the repeating decimal and put it equal to x.(say)

2) Write the number without using bar and equal to x.

3) Determine the number of digits having bar on their heads or number of digits before the bar for mixed recurring decimal.

4) If the repeating number is 1 then multiply by 10; if repeating number is 10 then multiply by 100 and so on.

5) Subtract the equation formed by step 2 and step 4.

6) Then find the value of x in the simplest form.

Example 1:

Express 0.2 in p / q form. Solution :

Let x = 0.2222 ------> (1)

Multiply equation (1) by 10 as there is only one number is repeating.

10 x = 2.2222 ------> (2)

Subtract equation (1) from (2)

9x = 2 ( dividing both side by 9)

x = 2 / 9