State true or false. All decimal numbers are also rational numbers.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The statement says that all decimal numbers are rational numbers and we have to decide if this is true or not.
Now, as per the definition, a rational number is of a fraction or a ratio of two integers, i.e.,

p q

, where p and q are integers and q is always positive and non-zero.
Also, it is a fact that every decimal number can be expressed as a fraction by shifting the decimals to the right of the given number till it becomes an integer and introducing a denominator with as much power of 10 as the number of places the decimal point shifts.
Example-

0.4 = 410 = 25

So, we conclude that any decimal can be expressed as a fraction and so all decimal numbers are also rational numbers.
Hence, the statement is true.
Hence the correct option is (1).

Watch 3-min video & get full concept clarity