# Interactive video lesson plan for: Convert decimal expansion in rational form p/q where q is not zero | Rational Form of decimal

#### Activity overview:

Convert decimal expansion in rational form p/q wehere q is not zero | Rational Form

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In the above discussion, we have seen that a rational number of the form has either a
terminating decimal expansion or a non - terminating repeating decimal expansion and
conversely that a terminating or a non - terminating and repeating decimal expansion can
be converted into the form p/q , where p and q are integers , and q is not zero 0 .

A terminating or a non - terminating and repeating decimal expansion can be converted into the form p/q, where p and q are integers , and q is not 0 .
00:02 Q3. Express the following in the form p/q, where p and q are integers and q is not 0.
00:18 (i) Express decimal form of a number 0.6666.. in rational form p/q.
00:39 Multiplying both sides of equation by 10.
Here, one digit 6 is repeating
02:05 rational form p/q of decimal form 0.6666....
02:15 (ii) Convert decimal form of a number 0.477777 in rational form p/q .
04:34 rational number of decimal expansion 0.477777 is 43/90.
(iii) Write decimal form of a number 0.001001001001.... in rational form p/q
05:26 Multiplying both sides of equation by 1000.
Here, three digits 001 is repeating.

A number whose decimal expansion is terminating or non-terminating recurring is rational.

06:52 Q4. Express decimal expansion 0.99999 .... in the rational form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
07:49 Multiplying both sides of equation by 10.
Here, one digit 9 is repeating
08:11 Subtract one equation from other
08:04 rational form p/q of decimal expansion 0.99999 .... is 1.

ecimal Expansion of Rational Numbers
Let us explain the process process of long division through some examples:
We apply the process of long division and obtain the decimal expansions as
shown below:

First find the decimal expansion of positive number and then put (-) sign

we first find the decimal expansion of positive numbers 5/3 and then put a bar '-'

Let us now learn to express decimal form of a number in rational form p/q where p and q
are integers and q is not 0.
when the decimal expansion is terminating
When the decimal expansion is non-terminating repeating
In the above discussion, we have seen that a rational number of the form p/q has either a
terminating decimal expansion or a non - terminating repeating decimal expansion and
conversely that a terminating or a non - terminating and repeating decimal expansion can
be converted into the form p/q, where p and q are integers , and q is not 0 .
Real Numbers and their Decimal Expansions
rational and irrational numbers
decimal expansions of real numbers
use the expansions to distinguish between rationals and irrationals
how to visualise the representation of real numbers on the number line using their decimal expansions.
Find the decimal expansions of

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