Question

7.484848…, Classify the given number as rational or irrational.

Answer 1

Given decimal 7.484848...

is a non-terminating recurring

decimal.

Therefore ,

7.4848....is a rational number.

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The set of digits which repeats

in non-terminating recurring

decimal is called period.

The number of digits in a period

of non-terminating decimal is

called periodicity .

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In 7.484848.....

Period = 48

Periodicity = 2

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Let x = 7.484848... ----( 1 )

Multiply ( 1 ) with 100, we get

100x = 748.484848...---( 2 )

Subtract ( 1 ) from ( 2 ) , we get

99x = 741

=> x = 741/99

= 247/33 [ p/q form ]

Therefore ,

7.484848....= 247/33

is a rational number.

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Answer 2

Answer:

GIVEN DECIMAL 7.484848...

IT IS A NON TERMINATING RECURRING DECIMAL ....

THEREFORE,

7.484848....is a rational number