1.

The decimal expansion of rational numbers is either terminating or non-terminating and recurring (repeating).(a) True(b) FalseThe question was posed to me in an international level competition.My question is taken from Real Numbers and their Decimal Expansions in section Number Systems of Mathematics – Class 9

Answer»

Correct option is (a) True

The best I can explain: Let’s take a known rational number to understand this.

For example, 3/4

We know that 3/4 is a rational number because both 3 and 4 are natural

numbers and 3/4=0.75 which is TERMINATING expansion.

Now, let’s take ONE example of non-terminating and recurring expansion.

For example 0.5787878…

Let x=0.5787878…

Then 100x=57.878787…

100x=57.3 + 0.5787878…

100x=57.3 + x

99x=57.3

Then, x=57.3/99

x=573/990

This is of the form of p/q where p and q are natural numbers. Hence we can SAY that .5787878… is rational number.

Hence, we can conclude that the DECIMAL expansion of rational numbers is either terminating or non-terminating and recurring (REPEATING).

We can also conclude that ‘The decimal expansion of irrational numbers is non-terminating and non-recurring.’


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